Simple interest

13 

Simple interest 

VCEcoverage 

Area of study 

Units 3 & 4 • Business 

related 

mathematics 

In this cha 

chapter pter 

13A Simple interest 

13B Finding P, r and T 

13C Bonds, debentures and 

term deposits 

13D Bank savings accounts 

13E Hire-purchase 

13F Effective rate of interest

608 Further Mathematics 


People often wish to buy goods and services that they cannot afford to pay for at the 

time, but which they are confident they can pay for over a period of time. The options 

open to these people include paying by credit card (usually at a very high interest rate), 

lay-by (where the goods are paid off over a period of time with no interest charged but 

no access to or use of the goods until the last payment is made), hire-purchase, or a 

loan from the bank. 

The last two options usually attract what is called simple interest. This is the amount of 

money charged by the financial institution for the use of its money. It is calculated as a 

percentage of the money borrowed multiplied by the number of periods (usually years) 

over which the money is borrowed. 

As an example, Monica wished to purchase a television for $550, but did not have 

the ready cash to pay for it. She made an agreement to borrow the money from a bank 

at 12% p.a. (per year) simple interest and pay it back over a period of 5 years. The 

amount of interest Monica would be charged on top of the $550 is 

$550 × 12% × 5 years which is $330. 

Therefore, Monica is really paying $550 + $330 = $880 for the television.

Chapter 13 Simple interest 609 

Total amount of loan or investment = Initial amount or Principal + Interest 

(charged or earned) 

A = P + I 

It would have been more economical for Monica to buy the television for cash at the 

time. However, by borrowing the money she has use of the television while she is 

paying it off. Also, by using this method she would be paying a small amount each 

month which is easy to budget for. The down-side is that she must pay the extra 

interest. 

Simple interest is the percentage of the amount borrowed or invested multiplied by 

the number of time periods (usually years). The amount is added to the principal either 

as payment for the use of the money borrowed or as return on money invested. 

I 

= 

PrT 

--------- 

100 

I = Simple interest charged or earned ($) 

P = Principal (money invested or loaned) ($) 

r = Rate of interest per period (% per period) 

T = Time, the number of periods (years, months, days) over 

which the agreement operates 

Hint: The interest rate, r, and time period, T, must be stated and calculated in the same 

time terms, for example: 

1 

4% per annum for 18 months must be calculated over 1 -- years, as the interest 

2 

rate period is stated in years (per annum); 

1% per month for 2 years must be calculated over 24 months, as the interest rate 

period is stated in months. 

Find the simple interest charged on borrowing $325 for 5 years at 3% p.a. (per annum or 

per year) interest. 

THINK WRITE 

1 

2 

3 

4 

5 

WORKED Example 

1 

Write the simple interest formula. I = 

List the values of P, r and T. Check that 

r and T are in the same time terms. 

PrT 

--------- 

100 

P = $325 

r = 3% per year 

T = 5 years 

Substitute into the formula. 

325 × 3× 5 

I = -------------------------- 

100 

Use a calculator to evaluate. I = 48.75 

Write your answer. The interest charged for borrowing $325 over 

5 years is $48.75.


Graphics Calculator tip! Simple interest calculations 

1. Transpose the formula for simple interest so that it 

PrT 

equals zero. (0 = I – --------- ). 

100 

2. Press MATH , choose 0: Solver then press the up 

arrow key and enter the equation. 

3. Press ENTER , then enter the values of the known 

variables and move the cursor to the variable to be 

solved for. The given values for worked example 1 

are shown in the screen at right. 

4. Press ALPHA [SOLVE]. 

Jan invested $210 with a building society in a fixed deposit account that paid 8% p.a. 

simple interest for 18 months. How much did she receive after the 18 months? 

THINK WRITE 

1 

2 

3 

4 

5 

6 


2 

Write the simple interest formula. 

PrT 

I = --------- 

100 

List the values of P, r and T. Check that P = $210 

r and T are in the same time terms. r = 8% p.a. 

Need to convert 18 months into years. T = 18 months 

1 

= 1 -- years 


210 8 1 

I = 

Use a calculator to evaluate. I = $25.20 

Add the interest to the principal (total A = P + I 

amount received). 

A = $210 + $25.20 

Write your answer. Total amount received at the end of the 

investment is $235.20. 

1 

× × -- 

2 

----------------------------- 

100 

2

WORKED 

Example 

1 

SkillSHEET 13.1 

SkillSHEET 13.2 

WORKED 

Example 

2 

remember 

remember 


1. Simple interest is the percentage of an amount borrowed or invested multiplied 

by the number of time periods, (usually years). The interest is added to the 

principal as payment for the use of the money or as return on the money 

invested. 

2. A = P + I where A = Total amount ($) 

P = Principal, or amount borrowed or invested ($) 


PrT 

3. I = --------- 

100 



r = Rate of interest earned per period (% per period) 

T = Time, the number of periods over which the 

agreement operates 

4. Interest rate, r, and time, T, must be stated and calculated in the same time 

terms. 

13A 


1 Find the interest charged on the following amounts borrowed for the 

periods and at the rates given. 

a $680 for 4 years at 5% p.a. b $210 for 3 years at 9% p.a. 

c $415 for 5 years at 7% p.a. d $460 at 12% p.a. for 2 years 

e 

g 

1 

$1020 at 12 -- % p.a. for 2 years 

2 

1 

$821 at 7 -- % p.a. for 3 years 

4 

f 

h 

3 

$713 at 6 -- % p.a. for 7 years 

4 

11.25% p.a. on $65 for 6 years 

i 6.15% p.a. on $21.25 for 9 years j 9.21% p.a. on $623.46 for 4 years 

k 

3 

13 -- % p.a. on $791.35 for 5 years. 

4 

2 Find the interest charged or earned on the following loans and investments: 

a $690 loaned at 12% p.a. simple interest for 15 months 

b $7500 invested for 3 years at 1% per month simple interest 

c $25 000 borrowed for 13 weeks at 0.1% per week simple interest 

3 

1 

d $250 invested at 1 -- % per month for 2 -- years. 

4 

EXCEL Spreadsheet 

3 Find the amount to which each investment has grown after the investment periods 

shown in the following examples: 

a $300 invested at 10% p.a. simple interest for 24 months 

b $750 invested for 3 years at 1% per month simple interest 

c $20 000 invested for 3 years and 6 months at 11% p.a. simple interest 

3 

d $15 invested at 6 -- % p.a. for 2 years and 8 months 

4 

1 

e $10.20 invested at 8 -- 

% p.a. for 208 weeks. 

2 

2 

Mathcad 


Simple 

interest 

GC program


4 

5 

6 

7 

8 

9 

10 

multiple ultiple choice 

If John had $63 in his bank account and earned 9% p.a. over 3 years, the simple 

interest earned would be: 

A $5.67 B $1701 C $17.01 D $22.68 E $27.00 


1 

If $720 was invested in a fixed deposit account earning 6 -- % p.a. for 5 years, the 

2 

interest earned at the end of 5 years would be: 

A $234.00 B $23 400.00 C $23.40 D $216.00 E $350.00 


A 4-year bond paid 7.6% p.a. simple interest. If Sonja bought a bond worth $550, the 

interest she earned would be: 

A $16.72 B $167.20 C $717.20 D $1672 E $30.40 


Bodgee Bank advertised a special offer. If a person invests $150 for 2 years, the bank 

will pay 12% p.a. simple interest on the money. At the expiry date, the investor would 

have earned: 

A $300 B $36 C $186 D $48 E $24 


Maclay invested $160 in a bank for 6 years earning 8% simple interest each year. At 

the end of the 6 years, he will receive in total: 

A $928 B $236.80 C $76.80 D $768 E $208 


1 

Simple interest was calculated on a term deposit of 4 years at 3 -- % per year. When 

2 

Ashleigh calculated the total return on her investment of $63.50, it was: 

A $72.39 B $7.75 C $71.24 D $8.89 E $75.50 


Joanne asked Sally for a loan of $125 to buy new shoes. Sally agreed on the condition 

that Joanne paid it back in two years at 3% p.a. simple interest. The amount Joanne 

paid Sally at the end of the two years was: 

A $200 B $7.50 C $130.50 D $132.50 E $128.75


11 multiple ultiple choice 

Betty invests $550 in an investment account earning 4% p.a. simple interest over 

6 years. Ron puts his $550 in a similar investment earning 5% p.a. simple interest for 

5 years. The difference in their earnings at the end of the investment period is: 

A $55 B $5.50 C $7.50 D $0 E $595 


Two banks pay simple interest on short-term deposits. Hales Bank pays 8% p.a. over 

5 years and Countrybank pays 10% p.a. for 4 years. The difference between the two 

banks’ final payout figure if $2000 was invested in each account is: 

A $0 B $800 C $2800 D $150 E $400 

13 Robyn wishes to purchase a new dress worth $350 to wear to the school formal. If she 

borrows the total amount from the bank and pays it off over 3 years at 11% p.a. 

simple interest, what is the total amount Robyn must pay back to the bank? 

1 

14 The Sharks Building Society offers loans at 8 -- % p.a. simple interest for a period of 

2 

18 months. Andrew borrows $200 from Sharks to buy Monique an engagement ring. 

Calculate the amount of interest Andrew is to pay over the 18 months. 

15 Silvio invested the $1500 he won in Lotto with an insurance company bond that pays 

1 

12 -- % p.a. simple interest provided he keeps the bond for 5 years. What is Silvio’s 

4 

total return from the bond at the end of the 5 years? 

16 The insurance company that Silvio used in the previous question allows people to withdraw 

part or all the money early. If this happens the insurance company will only pay 

3 

6 -- % p.a. simple interest on the amount which is withdrawn over the period it was invested 

4 

in the bond. The part which is left in the bond receives the original agreed interest. Silvio 

needed $700 for repairs to his car 2 years after he had invested the money but left the 

rest in for the full 5 years. How much interest did he earn from the bond in total? 

17 Jill and John decide to borrow money to improve their boat, but cannot 

agree which loan is the better value. They would like to borrow $2550. 

Jill goes to the Big-4 Bank and finds that they will lend her the money at 

1 

11 -- 

% p.a. simple interest for 3 years. John finds that the Friendly 

3 

Building Society will lend the $2550 to them at 1% per month simple 

interest for the 3 years. 

a Which institution offers the best rates over the 3 years? 

b Explain why.


Finding P, r and T 

In many cases we may wish to find the principal, interest rate or period of a loan. 

In these situations it is necessary to rearrange or transpose the simple interest 

formula after (or before) substitution, as the following example illustrates. 

A bank offers 9% p.a. simple interest on an investment. At the end of 4 years the interest 

earned was $215. How much was invested? 

THINK WRITE 

1 Write the simple interest formula. 

PrT 

I = --------- 

100 

2 List the values of I, r and T. Check that I = $215 

r and T are in the same time terms. r = 9% p.a. 

T = 4 years 

3 Substitute into the formula. 

P × r × T 

I = --------------------- 

100 

P × 9 × 4 

215 = --------------------- 

100 

4 Make P the subject by multiplying both 

sides by 100 and dividing both sides by 

(9 × 4). 

215 × 100 

P = ----------------------- 

9 × 4 

5 Use a calculator to evaluate. P = 597.22 

Write your answer. The amount invested was $597.22. 

6 


3 

Transposed simple interest formula 

It may be easier to use the transposed formula when finding P, r or T. 

Simple interest formula transposes: 

to find the principal 

P = 

100 × I 

----------------r× 

T 

to find the interest rate 

r = 

100 × I 

----------------- 

P × T 

to find the period of the loan or investment T = 

100 × I 

----------------- 

P × r


When $720 is invested for 36 months it earns $205.20 simple interest. Find the yearly 

interest rate. 

THINK WRITE/DISPLAY 


100 × I 

r = ---------------- 

P× T 

2 List the values of P, I and T. T must be P = $720 

expressed in years so that r can be I = $205.20 

evaluated in % per year. 

T = 36 months 

= 3 years 


100 × 205.20 

r = ------------------------------- 

720 × 3 

4 Evaluate on a calculator. Remember to 

bracket (720 × 3). 

5 


4 

Write your answer. The interest rate offered was 9.5% per annum. 

An amount of $255 was invested at 8.5% p.a. How long will it take, to the nearest year, to 

earn $86.70 in interest? 

THINK WRITE/DISPLAY 


100 × I 

T = ---------------- 

P× r 

2 Substitute the values of P, I and r. The 

rate, r is expressed per annum so time, P = $255 

T, will be evaluated in the same time I = $86.70 

terms, namely years. 

r = 8.5% p.a. 


100 × 86.70 

T = ---------------------------- 

255 × 8.5 

4 Evaluate on a calculator. Remember to 

bracket (255 × 8.5). 

5 


5 

Write your answer. The period of the investment was 4 years.

SkillSHEET 13.3 WORKED 

Mathcad 

Finding 

P, r 

and T 


Example 

3 

WORKED 

Example 

4 

WORKED 

Example 

5 

remember 

remember 

When finding P, r or T: 

1. substitute the given values into the formula and then rearrange to isolate the 

pronumeral, or 

2. transpose the simple interest formula 

100 × I 

(a) to find the principal 

P = ---------------r 

× T 

100 × I 

(b) to find the interest rate 

r = ---------------- 

P× T 

100 × I 

(c) to find the period of the loan or investment T = ---------------- 

P× r 

and substitute the given values into the transposed formula. 

13B 


1 For each of the following, find the principal invested. 

a Simple interest of 5% p.a., earning $307 interest over 2 years 

b Simple interest of 7% p.a., earning $1232 interest over 4 years 

c Simple interest of 8% p.a., earning $651 interest over 18 months 

1 

d Simple interest of 5 -- % p.a., earning $78 interest over 6 years 

2 

e Simple interest of 6.25% p.a., earning $625 interest over 4 years 

2 For each of the following, find the interest rate offered. Express rates in % per annum. 

a Loan of $10 000, with a $2000 interest charge, for 2 years 

b Investment of $5000, earning $1250 interest for 4 years 

c Loan of $150, with a $20 interest charge, for 2 months 

d Investment of $1400 earning $178.50 interest for 6 years 

1 

e Investment of $6250 earning $525 interest for 2 -- years 

3 For each of the following, find the period of time (to the nearest month) for which the 

principal was invested or borrowed. 

a Investment of $1000 at simple interest of 5% p.a. earning $50 

b Loan of $6000 at simple interest of 7% p.a. with an interest charge of $630 

c Loan of $100 at simple interest of 24% p.a. with an interest charge of $6 

1 

d Investment of $23 000 at simple interest of 6 -- % p.a. earning $10 465 

2 

e Loan of $1 500 000 at simple interest of 0.125% per month earning $1875 

4 Lennie Cavan earned $576 in interest when she invested in a fund paying 9.5% simple 

interest for 4 years. How much did Lennie invest originally? 

5 Lennie’s sister Lisa also earned $576 interest at 9% simple interest, but she only had 

to invest it for 3 years. What was Lisa’s initial investment? 

6 Jack Kahn put some money away for 5 years in a bank account which paid 3 -- 

% 

4 

interest. He found from his bank statement that he had earned $66. How much did 

Jack invest? 

2 

3


7 James needed to earn $225 in one year. He invested $2500 in an account earning 

simple interest at a rate of 4.5% p.a. paid monthly. How many months will it take 

James to achieve his aim? 

8 Carol has $3000 to invest. Her aim is to earn $450 in interest at a rate of 5% p.a. Over 

what term would she invest? 

9 

10 

11 

12 

13 


Peter borrowed $5000 and intended to pay it back in 3 years. The terms of the loan 

3 

indicated Peter was to pay 9 -- % p.a. interest. The interest Peter paid on the loan was: 

4 

A $146 250 B $446.25 C $1462.50 D $121.88 E $1211.88 


Joanne’s accountant found that 

for the past 2 years she had 

earned a total of $420 interest in 

an account paying 6% simple 

interest. When she calculated 

how much she invested the 

amount was: 

A $350 

B $3500 

C $50.40 

D $7000 

E $70.00 


A loan of $1000 is taken over 5 years. The simple interest is calculated monthly. The 

total amount repaid for this loan is $1800. The simple interest rate per year on this 

loan is closest to: 

A 8.9% B 16% C 36% D 5% E 11.1% 


Jarrod decides to buy a motorbike at no deposit and no repayments for 3 years. He 

takes out a loan of $12 800 and is charged at 7.5% p.a. simple interest over the 

3 years. The lump sum Jarrod has to pay in 3 years time is: 

A $960 B $13 760 C $2880 D $12 800 E $15 680 


1 

Chris and Jane each take out loans of $4500 and are offered 6 -- % p.a. simple interest 

4 

over a 3-year period. Chris’s interest is paid monthly whereas Jane’s is paid yearly. 

The difference in the total amount of interest each person pays after the 3 years is: 

A none B $877.50 C $10 530 D $9652.50 E $1000 

14 Alisha has $8900 that she is able to invest. She has a goal of earning at least $1100 in 

2 years or less. Do any of the following investments satisfy Alisha’s goal? 

a 10% p.a. for 15 months 

1 

b 4 -- 

% p.a. earning $1200 

4 

c After 100 weeks a final payout of $10 500 

d After 2 years at 0.6% per month


Bonds, debentures and term deposits 

Debentures 

If a company needs money, one option is for it to offer a debenture (a legal document 

detailing an investment agreement) for sale to the public. An investor will pay an 

amount of money (principal) to the company, and in return the company agrees to pay 

the investor interest at regular intervals (monthly, quarterly or yearly). At the end of the 

agreed term the principal is returned to the investor. The advantage of the debenture is 

two-fold: first, the company has the use of the money during the agreed period to make 

more money for the company and second, the investor knows what their return will be 

for each period and is guaranteed the return of the principal. 

Term deposits 

TOP INVESTOR RATES 

1 to 5 yr effective rates are shown in brackets. Source: CANNEX (Polifax 019 725 660). 

BEST BANK TERM DEPOSITS BEST OTHERS 

Period Bank 

Rate 

Period Institution Rate 

30 days HSBC 

4.70 

30 days GIO 

3.95 

90 days Arab Bank 5.00 

90 days GIO 

4.75 

180 days HSBC 

5.12 

180 days GIO 

4.95 

270 days Arab Bank 5.25 

270 days Greater BS/HC CU 5.00 

1 year Suncorp Metway 5.00 (5.58) 1 year GIO 

5.25 

2 years HSBC/PIBA 5.66/5.70 (5.78) 2 years GIO 

5.49 

3 years HSBC 

6.20 (6.20) 3 years AGC 

5.70 

4 years HSBC 

6.16 (6.30) 4 years Police CU 6.00 

5 years HSBC 

6.33 (6.48) 5 years AGC 

6.20 

Term deposits allow an investor to lend money to a bank or building society for a 

particular length of time. The money cannot be withdrawn during the agreed period but 

earns a better interest rate than in a normal savings account. At the end of the term the 

interest plus the principal is paid back to the investor. The advantage of the term deposit 

is that the money is secure and the interest rate is better than that on a savings account. 

The disadvantage, of course, is that if the money is needed during the period it cannot 

be withdrawn (except under special circumstances agreed to by the bank). 

Investment bonds 

Investment bonds are another form of investment which is offered to the investor by a 

bank or the government, and interest is paid on the investment monthly, quarterly, six 

monthly or annually. The one advantage is that the bond can be sold to someone else 

during the period before the maturation date. This allows the investor some flexibility if 

the money is needed during the period of investment. 

All the above investment types offer advantages to the investor and to the institution. 

The institution has the use of the money over a fixed period and the investor receives 

higher than normal interest. All of these investments carry some risk and individuals 

must decide on which type to use based on personal circumstances. 

Bonds, debentures and term deposits are simple interest accounts. 

(5.35) 

(5.60) 

(5.82) 

(6.09) 

(6.34)



Jaclyn buys $50 000 worth of debentures in a company. She earns 9.5% p.a. simple 

interest, paid to her quarterly (that is, every 3 months). If the agreed period of the 

debenture was 18 months: 

a calculate the amount of interest Jaclyn will earn for each quarter 

b calculate the total amount collected at the end of the term. 

THINK WRITE 

a 1 Write the simple interest formula. 

PrT 

a I = --------- 

100 

2 List the values of P, r and T. Convert P = $50 000 

the interest rate period to quarters. r = 9.5% per year 

= 9.5% ÷ 4 per quarter 

= 2.375% per quarter 

T = 1 quarter 

3 Substitute into the formula and 

evaluate. 

50 000 × 2.375 × 1 

I = -------------------------------------------- 

100 

= 1187.50 

4 Write your answer. Jaclyn will earn $1187.50 for each quarter. 

b 1 There are 6 quarters in 18 months. b Total interest = $1187.50 × 6 

Alternatively, use the simple interest 

= $7125 

formula with the new data. 

or 

50 000 × 2.375 × 6 

I = -------------------------------------------- 

100 

= 7125 

Write your answer. The total interest earned is $7125. 

2 

6 

Townbank offers a term deposit account paying investors 12.5% p.a. simple interest on 

investments over $100 000 for 2 years or more. Peta decides to invest $150 000 in this 

account for 2 years. How much interest will Peta earn at the end of the investment? 

THINK WRITE 

1 

2 


7 


List the values of P, r and T. Check that 

r and T are described in the same time 

terms. 

Substitute into the formula and 

evaluate. 

PrT 

--------- 

100 

P = $150 000 

r = 12.5% p.a. 

T = 2 years 

3 150 000 × 12.5 × 2 

I = -------------------------------------------- 

100 

= $37 500 

4 Write your answer. Peta’s $150 000 invested for 2 years will 

earn $37 500.

Mathcad 


GC program 








An investment bond is offered to the public at 9% p.a. Louise buys a bond worth $2000 

that will mature in 2 years. How much in total will Louise receive at the end of the 2 years? 

THINK WRITE 

1 

2 

3 

4 

5 

6 

WORKED 

Example 

6 

WORKED 

Example 

7 

WORKED 

Example 

8 


8 

Write the simple interest formula. 

PrT 

I = --------- 

100 

List the values of P, r and T. P = $2000 

r = 9% p.a. 

T = 2 years 


2000 × 9 × 2 

I = ----------------------------- 

100 

Use a calculator to evaluate. I = $360 

Add interest to principal. A = P + I 

A = 2000 + 360 

= 2360 

Write your answer. The $2000 investment bond will mature at the 

end of 2 years to a total of $2360 at simple 

interest of 9% p.a. 

remember 

remember 

1. Simple interest accounts include bonds, debentures and term deposits. 

2. Read the question carefully: does it ask for the interest or the final total 

amount? 

13C 

Bonds, debentures and 

term deposits 

1 Spice Clothing company offers debentures paying 8% p.a. interest paid quarterly for a 

period of 2 years. When $20 000 worth of Spice debentures are purchased, calculate 

the total return on the investment. 

2 Harry decided to invest $2000 in a term deposit for 18 months. The bank offered 

10.5% p.a. interest paid each half-year. Calculate the interest Harry would earn on the 

investment. 

3 An investment bond is advertised as paying 10 -- 

% p.a. interest on a 3-year invest- 

2 

ment. Elise purchased a bond for $3000, but needed to sell it after 18 months. How 

much will Elise receive at the end of her 18-month investment? 

4 Rabbit debentures, worth $10 000, were purchased for a period of 15 months. The 

debenture paid 12% p.a., payable each 3 months. What was the investment worth at 

the end of the 15 months? 

1


5 JNK Bank offers term deposits on amounts above $5000 at 12% p.a. simple interest 

payable each quarter for periods longer than 2 years. Mr Smith invests $6000 in this 

1 

term deposit for 2 -- years. What is Mr Smith’s final return on his money? 

6 Mark purchases a $2500 investment bond earning 12 -- % p.a. interest paid yearly. 

4 

The bond matures after 2 years. 

What interest will Mark earn? 

7 

8 

9 

10 

11 

2 


Debentures in TRADEX are issued at 9% p.a. simple interest. The interest gained on 

an investment of $7000 over 3 years would be: 

A $630 B $1890 C $18 900 D $7630 E $21 000 


The rate of interest on a term deposit for 3 months is 4.25% per year. If $10 000 is 

invested in the term deposit, the amount of interest earned over the 3 months is: 

A $106.25 B $425 C $141.67 D $1062.50 E $1275 


1 

State government bonds pay interest of 7 -- % p.a. simple interest. Philippa invested 

4 

$2500 in the bonds which mature in 5 years. Philippa’s income each quarter would be: 

A $181.25 B $2718.77 C $45.31 D $725 E $72.50 


1 

ElCorp offers company debentures earning 8 -- % p.a. interest for an investment of 

2 

$5000 for 2 years. The interest on the investment is: 

A $170 B $212.50 C $825 D $850 E $85 


A term deposit is advertised stating that if $2500 is invested for 2 years the interest 

earned is $285. The rate of interest per annum is: 

A 10% B 17.5% C 5.7% D 11.4% E 10.5% 

1

WorkSHEET13.1 


12 

13 


An investment bond of $7500 pays interest of $1125 at 3.75% p.a. interest. The time 

the bond is taken for is: 

1 

1 

A 3 years B 4 -- years C 3 -- years D 4 years E 5 years 

2 


A principal amount is invested in a bond that will accumulate to a total of $64 365 

1 

after 4 months at 6 -- % p.a. The principal is: 

2 

A $60 000 B $63 000 C $6300 D $50 000 E $5000 

14 The following term deposit rates were advertised in a magazine 

Toni Ford had $5500 to invest. Calculate her 

return if she invested the money in a term 

deposit with this bank for: 

a 35 days 

b 120 days 

c 1 year. 

Hint: Express days as a fraction of a year. 

Term Rate 

30–59 days 4.2% p.a. 

60–149 days 4.7% p.a. 

150–269 days 5.0% p.a. 

270–365 days 5.4% p.a. 

15 Dennis and Delia have $7500 to invest. They know that they will need the money in 

18 months but are not sure how to invest it. While reading a magazine, they see the 

following three advertisements: 

1 

i investment bonds offered at 12 -- % p.a. interest paid each 6 months 

2 

ii debentures in a company paying 12% p.a. with interest paid each quarter 

3 

iii a term deposit paying 11 -- % p.a. interest paid each 3 months. 

4 

a Calculate their total return on each investment. 

b What did you notice about the time in which the interest was calculated? 

2

Bank savings accounts 

Most banks offer their customers savings accounts with 

interest that is usually paid on 

1. the minimum monthly balance, or 

2. the daily balance. 

The interest is added at a specified time — say once or 

twice a year — as nominated by the bank, for example, 

on the first day of June and December of each year. The 

more frequently the interest is added, the better for the 

customers. 


Savings accounts — minimum monthly balances 

To calculate interest on a minimum monthly balance saving account, the bank looks at 

the balances of the account for each month and calculates the interest on the smallest 

balance that appears in each month. 


9 

At the beginning of March, Ryan had $621 in his savings bank account. On 10 March he 

deposited $60. If the bank pays 8% p.a. interest paid monthly and calculated on the 

minimum monthly balance, calculate the interest Ryan earns in March. 

THINK WRITE 

1 The smallest balance for March is 

$621, as the only other transaction in 

that month increased the balance. 

Minimum monthly balance for March is $621. 


PrT 

I = --------- 

100 

3 List the values of P, with r and T in P = $621 

months. 

8 

r = ----- % per month 

12 

T = 1 month 

4 Substitute into the formula and 

evaluate. 

8 

621 × ----- × 1 12 

I = ---------------------------- 

100 

= 4.14 

5 Write your answer. The interest earned for the month of March 

was $4.14.


The minimum monthly balance method is used in the next worked example. 

Minimum monthly balance method 

Date Deposit Withdrawal Balance 

3/7 

7/7 

21/7 

28/7 

$100 

$500 

$ 50 

$678 

$337.50 

$837.50 

$159.50 

$209.50 

The above passbook page shows the transactions for July. Find the interest that will be 

earned in July if the bank pays 7% p.a. simple interest on the minimum monthly balance. 

THINK WRITE 

1 

2 

3 

To find the smallest balance for July, 

look at all the running balances. Also 

check balances at the start and end of 

the month. Notice that the balance on 

1 and 2 July, if shown, would have been 

$237.50. 


List the values of P, r and T in months. P = $159.50 

7 

r = ----- % per month 

12 

T = 1 month 

Substitute into the formula and 

7 

× ----- × 1 12 

evaluate. I = ----------------------------------- 

100 

= 0.93 

Minimum monthly balance for July is $159.50. 

PrT 

--------- 

100 

4 159.50 

5 


10 

Write your answer. The interest earned for July was $0.93. 

Savings accounts — daily balances 

To calculate the interest on a daily balance saving account, the bank looks at the 

balances of the account. The number of days each balance is maintained is used to 

calculate the interest. When doing these calculations for yourself, you need to set out 

your workings carefully, for example using tables. 

Let’s investigate worked example 10 again, using the daily balance method.


Daily balance method 

Use the daily balance method to find the interest that will be earned in July, if the bank 

pays 7% p.a. simple interest on the daily balance. 

THINK WRITE 

1 

2 

3 

4 

5 


Set up a table showing each new 

balance and the number of days 

the balance applies. Look at all 

running balances including those 

for 1 and 31 July. 

Calculate the interest for each 

balance. As the interest rate is in % 

per annum, express the number of 

days as a fraction of a year; for 

2 

example, 2 days = -------- of a year. 

Sum the interest. The calculations 

were to hundredths of a cent for 

accuracy. 

365 

11 

Balance 

$ 

Number 

of days 

the 

balance 

applies 

Interest for month = $2.9734 


calculations 

$ 

Round off to the nearest cent. $2.9734 ≈ $2.97 

Write your answer. The interest earned for July was $2.97. 

Interest 

earned 

$ 

237.50 × 7 × -------- 

$237.50 2 365 

------------------------------------- $0.0911 

100 

337.50 × 7 × -------- 

$337.50 4 365 

------------------------------------- $0.2589 

100 

837.50 × 7 × -------- 

$837.50 14 365 

------------------------------------- $2.2486 

100 

159.50 × 7 × -------- 

$159.50 7 365 

------------------------------------- $0.2141 

100 

209.50 × 7 × -------- 

$209.50 4 365 

------------------------------------- $0.1607 

100 

The daily balance method offers more interest than the minimum monthly 

balance method, as it credits the customer for all monies in the account, including 

the $600 deposited for 14 days. 

remember 

remember 

1. Two methods used by banks for calculating interest on savings accounts are: 

(a) minimum monthly balances 

(b) daily balances. 

2. Daily balances offer the best interest rate for investors. 

3. Look at the balances on the first and last day of the month when establishing 

the minimum monthly balance or daily balances. 

1 

4. Express days as a fraction of a year; for example, 1 day = -------- of a year. 

365 

2 

4 

14 

7 

4

GC program 





WORKED 

Example 

9 

Mathcad 


Example 

10 

SkillSHEET 13.4 WORKED 

WORKED 

Example 

11 

Bank savings accounts 

1 A bank savings passbook showed that the opening balance for the month was $2150. 

That month Paul paid the following bills out of the account: 

Electricity $21.60 Telephone $10.30 Rent $52.00 

Paul also deposited his wage of $620 for the month into the account. 

a What was Paul’s minimum monthly balance? 

b If the bank pays 5.5% p.a. paid monthly on the minimum monthly balance, how 

much interest did Paul earn in the month? 

2 Date Deposit Withdrawal Balance 

1/5 

3/5 

7/5 

19/5 

27/5 

13D 

$12 

$10 

$16 

$ 8 

$27.50 

$39.50 

$23.50 

$15.50 

$25.50 

Roberta’s passbook shows the above transactions for May. Find the interest Roberta 

will earn in May if the bank pays 6% p.a. simple interest: 

a on the minimum monthly balance 

b on the daily balance. 

3 For the month of July, Rhonda received $3.20 in interest on her savings account. 

Rhonda’s minimum balance in July was $426.20. What was the per annum simple 

interest rate offered by the bank? 

4 Kristen receives the following statement from her bank. Due to a computer error the 

interest and balances were not calculated. 

Kristen rang the bank and was told that she received interest at a rate of 6 -- 

% p.a. paid 

monthly on her minimum monthly balance. Copy out Kristen’s statement and fill in the 

balances and interest payments. 

1998 Transaction Debit Credit Balance 

1 May Balance B/F 2132.20 

3 May Cheq 4217 460.27 

7 May Deposit 230.16 

17 May Cheq 4218 891.20 

26 May Wages 1740.60 

31 May Interest _______ 

2 June Deposit 415.10 

8 June Cheq 4220 2217.00 

19 June Cheq 4219 428.50 

21 June Cheq 4222 16.80 

23 June Wages 1740.60 

30 June Interest _______ 

1 July Deposit 22.80 

4 July Cheq 4221 36.72 

18 July Cheq 4223 280.96 

26 July Wages 1740.60 

31 July Interest _______ 

3 

4

c 


5 Using the bank statement from question 4, another bank offers to show Kristen that 

daily balance interest credited each quarter is more rewarding. The interest is still 

6.75% p.a. but is only credited at the end of the quarter, that is, on 31 July. Calculate: 

a the interest for the quarter ending July 

b the increase in interest earned using the daily balance method. 

Hint: This could be done using a spreadsheet. See the section on Spreadsheet Applications 

later in this chapter. 

6 Clark Kent has the following income and expenses for August and September. 

Income: $1410.20 salary each fortnight beginning 4 August 

$461.27 income tax refund on 5 September 

$68.20 cheque from health fund on 10 August 

Expenses: $620.80 rent on 20 August and 20 September 

$180.64 telephone account on 2 September 

$150.26 electricity account on 15 August 

$180.00 Visa account on 30 August 

$327.60 health fund on 5 August and 5 September 

Draw up a statement (as for question 4) for Clark, remembering that he receives 

1 

7 -- % interest paid on the last day of each month on the minimum monthly balance in 

2 

the account. 

1 

7 If the savings interest rate is 2 -- 

% p.a., calculate the interest credited at the end of each 

2 

quarter for the following accounts using: 

i the minimum monthly balance 

ii the daily balance. 

Also calculate: 

iii the increase in interest earned using the daily rather than the minimum monthly 

balance method. 

a 3rd quarter statement for July, August and September 


3/7 

$100 $ 750.00 

7/8 

$ 500 

$ 1250.00 

21/8 

$ 670 

$ 1920.00 

28/8 

$420 $ 1500.00 

20/9 

$10 000 

$11 500.00 

b 1st quarter statement for January, February and March in 2000 


31/12/1999 $100 

$400.00 

1/2/2000 

$600 

? 

1/3/2000 

$100 

? 

28/3/2000 

$ 50 

? 


3/10 

17/12 

21/12 

22/12 

28/12 

$2100 

$3500 

$1900 

$400 

$650 

$2450.00 

$5950.00 

$4050.00 

$3650.00 

$3000.00


Hire-purchase 

People buy on hire-purchase when they cannot afford to buy the goods for cash. 

A deposit is usually paid and the balance is paid over a fixed period of time. The 

retailer arranges a contract with a financial institution and the purchaser pays 

regular instalments including interest at a flat rate to the financial institution. 

A flat rate is the same as simple interest rate. 

The interest charged is added onto the balance owing and then divided into the equal 

instalments. 

Advantages of this form of buying are: 

1. the purchaser has the use of the goods while paying them off 

2. the cost of the goods is spread over a long term in small amounts. 

The disadvantages are more complex: 

1. the purchaser pays more for the goods in the long run 

2. the goods are legally owned by the finance company until they are fully paid off 

3. any forfeit on making the regular payments entitles the finance company to repossess 

the goods as well as retain all past payments made. 

The main stages of hire-purchase interest and total price calculations are: 

Step 1. Check the price of the goods. 

Step 2. Pay any deposit. 

Step 3. Set up the balance as a loan. 

Loan amount = price of goods − deposit 

Step 4. Calculate the interest on the loan using the simple interest formula. 

Step 5. The total amount to be repaid is the sum of the balance and the interest. 

Step 6. Establish regular payments/instalments. 

total amount 

Instalment amount = ---------------------------------------------------number 

of instalments 

Step 7. Total cost of goods = deposit + loan amount + interest 

or = deposit + instalment amount × number of instalments

A sapphire ring with a marked price of $1800 

is offered to the purchaser on the following 

terms: $200 deposit and the balance to be 

paid over 24 equal monthly instalments with 

interest charged at 11.5% p.a. flat rate. Find: 

a the total interest paid 

b the monthly repayments. 


THINK WRITE 

a 1 Write the cash price. a Cash price = $1800 

2 Determine the deposit. Deposit = $200 

3 Calculate the amount of the loan Balance or loan amount = cash price − deposit 

required. 

= $1800 − $200 

= $1600 

4 List P, r and T. P = $1600 

r = 11.5% p.a. 

T = 2 years 

5 Write the simple interest formula, 

substitute into it and evaluate. 

PrT 

I = --------- 

100 

1600 × 11.5 × 2 

I = ------------------------------------- 

100 

I = $368 

6 Write your answer. Total interest to be paid is $368. 

b 1 Add the interest to the principal. b Total repayment amount = $1600 + $368 

= $1968 

2 Calculate the monthly repayments. 

total amount 

Regular payment = ----------------------------------------------------number 

of repayments 

$1968 

= -------------- 

24 

= $82 

3 


12 

Write your answer. The regular monthly repayments are $82.



A car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit 

of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. 

Interest is charged at 12% p.a. 

a What is the monthly instalment? b What is the total cost of the car? 

THINK WRITE 

a 1 Write the cash price. a Cash price = $21 000 

2 Calculate the deposit, that is, 10% of Deposit = 10% × $21 000 

$21 000. 

= $2100 

3 Calculate the amount of the loan Loan amount = $21 000 − $2100 

required. 

= $18 900 

4 List P, r, and T. Check that r and T P = $18 900 

are in the same time terms. Convert r = 12% p.a. 

the time period into years to match T = 60 months 

the % rate per annum. 

= 5 years 

5 Write the simple interest formula, 

substitute into it and evaluate. 

PrT 

I = --------- 

100 

18 900 × 12 × 5 

I = ------------------------------------ 

100 

I = 11 340 

6 Add the interest to the principal to find Total amount = 18 900 + 11 340 

the total amount of the loan to be repaid. 

= $30 240 

7 Calculate the monthly instalment. 

total amount 

Regular payment = ----------------------------------------------------number 

of repayments 

$30 240 

= ------------------ 

60 

= $504 

8 Write your answer. The monthly instalment is $504. 

b 1 Calculate the cost of the car. b Total cost = deposit + instalment amount 

× number of instalments 

= 2100 + 504 × 60 

= $32 340 

or 

Total cost = deposit + loan + interest 

= 2100 + 18 900 + 11 340 

= $32 340 

Write your answer. The total cost of the car is $32 340. 

2 

13 

Weekly instalment advertising 

Many retailers use the option of hire-purchase to attract new sales. They also choose to 

advertise the instalment amount as it can seem to be very manageable. Buyers should 

investigate the entire arrangement offered and find answers to questions such as: 

1. What is the interest rate? 

2. How does it compare to bank rates? 

3. What is the total cost of the item? 

4. How much interest is charged?


14 

The following advertisement for a computer was found 

in a newspaper. 

Computer for sale 

Cash price $3695 

or pay only a third deposit and 

104 weekly instalments of only $25.97. 

If there is a total of 104 weekly instalments and a third 

deposit, find: 

a the interest charged 

b the interest rate 

c the total cost of the computer. 


THINK WRITE 

a 1 Write the cash price. a Cash price = $3695 

2 Calculate the deposit. 

1 

Deposit = -- of $3695 

3 

= $1231.67 

3 Calculate the amount of the loan. Loan amount = $3695.00 − $1231.67 

= $2463.33 

4 Calculate the total cost of the loan, that Total cost of loan = $25.97 × 104 

is, the total of the loan and the interest 

charged paid by weekly instalments. 

= $2700.88 

5 Calculate the interest charged and Interest charged = total amount − loan 

write your answer. 

I = A − P 

= 2700.88 − 2463.33 

= 237.55 

Interest on the $2463.33 loan is $237.55 

b 1 Use the transposed simple interest b P = $2463.33 

formula to find r, the interest rate on I = $237.55 

the loan. Check that T is expressed T = 104 weeks 

in years to evaluate the interest rate = 2 years 

in % per annum. 

100 × I 

r = ---------------- 

P× T 

100 × 237.55 

r = ------------------------------- 

2463.33 × 2 

= 4.82 . . . 

2 Write your answer. The interest rate for this hire-purchase is 

4.8% p.a. 

c 1 Calculate the total cost of the c Total cost = deposit + loan + interest 

computer. 

= 1231.67 + 2463.33 + 237.55 

= $3932.55 

2 Write your answer. The total cost for the computer including 

interest on the loan is $3932.55.


WORKED 

Example 

12 

WORKED 

Example 

13 

WORKED 

Example 

14 

remember 

remember 

The main stages of interest and total price calculations are: 

1. Loan amount = price of goods − deposit 

2. Flat rate interest on the loan is calculated using the simple interest formula. 

total amount 

3. Instalment amount = --------------------------------------------------number 


4. Total cost of goods = deposit + loan amount + interest 

or = deposit + instalment amount × number of instalments 

13E 

Hire-purchase 

1 Debbie and Peter purchased a lounge suite on hire-purchase. The cash price was 

$2500. Peter and Debbie paid $250 deposit and signed an agreement to pay the 

balance in 36 equal monthly instalments. If the hire-purchase company charges 14% 

p.a. simple interest, find: 

a the total interest paid 

b the monthly repayments. 

2 When buying new appliances for a recently renovated kitchen, Cheryl bought, from 

the same supplier, a refrigerator worth $490, a stove worth $350 and a dishwasher 

worth $890. If she paid $450 deposit and paid the balance over 48 months in equal 

monthly instalments at 12% p.a. simple interest, find: 

a Cheryl’s monthly instalments 

b the total amount Cheryl paid for the goods. 

3 While on holidays in Noosa, Jan saw a bracelet she could not live without. The 

marked price was $2000. The jewellery shop owner offered her a discount of 15% if 

she paid a deposit of $250. Jan paid the deposit and signed a hire-purchase agreement 

that she would pay the balance of the bracelet’s cost at 15% p.a. flat rate with 24 equal 

monthly instalments. 

a What was the price of the bracelet after the 15% discount? 

b Calculate the balance Jan was to pay back. 

c Calculate the interest Jan paid. 

d Calculate Jan’s monthly instalment. 

e How much did Jan pay altogether for the bracelet? 

4 The cash price of a suit is $1800. If a customer pays a deposit of $300 and pays equal 

monthly instalments of $60 over 2 -- 

years, calculate: 

1 

2 

a the amount of interest charged 

b the flat rate of interest 

c the total paid for the suit. 

5 A car has a marked price of $7500. The dealer gives two choices of payment: 

i no deposit, with the $7500 paid in equal monthly instalments of $250 for 3 years 

ii $1500 deposit, paying interest of 12% p.a. and making equal monthly repayments 

for 3 years. 

a Calculate the interest rate in choice i. 

b Which deal is best for the purchaser? Why?



An electric guitar is bought on hire-purchase for a $250 deposit 

and monthly instalments of $78.50 for 3 years. The cash price 

for this guitar is $2500. The interest rate is closest to: 

A 9.5% B 7% C 8.5% D 8% E 7.5% 


‘Carpeting the home is not cheap’, Rob stated. 

‘Hire-purchase is the answer’, replied Tom. 

The cost of the carpet for the house is $9500. Rob and Tom 

place a deposit of $1500 and plan to pay it back weekly over 

4 years at 13% interest per year. The weekly instalment is: 

A $253.37 B $62.20 C $46.20 D $58.46 E $462.00 


A salesman told a couple that if they bought a television at $890 today, he would 

allow a deposit of $100 plus $8.65 weekly for 2 years. The interest rate charged is: 

A 10% B 7% C 6.5% 

1 

D 9 -- % 

2 

E 7.5% 

9 For the video camera in the advertisement, find: 

i the total paid 

ii the interest rate for both Option a and Option b. 

THIS VIIDEOO CAAMERA CAN BE YOURS. 

EEASY TEERMS 

CASH PRICE $780 

or OOption a 

NO DEPOSIT AAND $37.7700 

MONTHLLY PAYMEENTTSS 

FOR 2 YEARRS 

or Option b 

$100 DEPOSIITT AAND $$26.72 

PAID MONTHHLY FOR 3300 MONTHS 

10 A company advertised a dining room suite for $2500. You could pay: 

a cash and receive a 10% discount, or 

b $200 deposit and 5% p.a. interest on the remainder for 3 years, or 

c $300 deposit and 4.5% p.a. on the remainder for 3 -- 

years, or 

d $400 deposit and 4% p.a. interest on the remainder for 4 years. 

What is the total paid on each deal? 

11 Carefully read the advertisement at right for 

the cash price and regular instalments for the 

colour television. The term of the repayments 

is for 3 years with 20% deposit. 

Calculate: 

a the flat interest rate 

b the total cost of the TV under the hirepurchase 

plan 

c the increase in cost over a cash sale. 

1 

2 

$1095 or $15.40 fortnightly


Effective rate of interest 

When purchasing goods on hire-purchase or through a personal loan, the finance 

company lending the money hopes to make the deal look as attractive as possible. 

Some details, therefore, are not prominently stated to the customer. One such detail 

is the effective rate of interest. The amount borrowed reduces over the term of the 

loan, but the customer is still paying interest on the total initial loan amount. The 

effective interest rate is the equivalent reducing balance interest rate taken over the 

contract period. 

There are two ways of converting flat rate to effective rate. 

1. Estimation 

Effective interest rate is a little less than 2 × flat interest rate. 

2. Calculation 

2n 

Effective interest rate = ----------- × flat rate where n is the number of payments. 

n + 1 

That is, on a loan of $100 at 10% interest over 4 years with yearly repayments, the 

interest charged is: 

I = 100 × 0.10 × 4 = $40. 

2× 4 

The effective interest rate is ----------- 

× 10% = 16% (assuming yearly repayment). 

4+ 1 

This means that, even though the person is paying $40 interest, the effective interest 

rate over the period is actually 16%, not 10%. The longer the period of the loan, the 

higher the effective interest rate. This is shown clearly in the following table. 

Year 

Principal 

owing 

$10,000 

PERSONAL LOAN 

Repayment 

of principal 

$149 

from per fortnight 

Based on a 3 year term at a fixed rate of 9.95%* p.a. 

Flat rate of 

interest paid 

Total interest $40 Flat rate 10% Effective rate 16% 

Effective rate of 

interest paid 

1 100 25 10% of 100 = 10 16% of 100 = 16 

2 75 25 10% of 100 = 10 16% of 75 = 12 

3 50 25 10% of 100 = 10 16% of 50 = 8 

4 25 25 10% of 100 = 10 16% of 25 = 4 

$100 $40 $40


Jason decides to borrow money for a holiday. If a personal loan is taken over 4 years with 

equal quarterly repayments at 12% p.a. flat rate (simple interest), calculate the effective 

rate of interest. 

THINK WRITE 

1 

2 

3 

4 


15 

Write the flat rate and number of 

instalments. 

Flat rate = 12% 

n = 4 × 4 

= 16 

Write the formula for effective rate of 

interest. 

2n 

Effective rate = ----------- × flat rate 

n + 1 

Substitute n = 16 and r = 12. 

2× 16 

Effective rate = -------------- × 12 

16 + 1 

Write your answer. Check the answer 

by estimating the rate which is less than 

2 × 12% (or 24%) p.a. 

remember 

remember 

= 22.588 

The effective interest rate is 22.6% p.a. for a flat 

rate loan of 12% with sixteen instalments. 

1. The effective interest rate is a true indication of the interest rate on a loan that 

is calculated using a flat interest rate when the loan is progressively being 

reduced, such as in hire-purchases. 

2. Estimation of effective interest: 

Effective interest rate is a little less than 2 × flat interst rate. 

Calculation of effective interest: 

2n 

Effective interest rate = ----------- × flat rate where n is the number of payments. 

n + 1 

3. The fewer the payments, the closer the flat rate is to being a true indication of 

the rate charged. 

For example, 12% flat rate with 1 payment only: 

2× 1 

Effective rate = ----------- × 12% = 12% 

1+ 1



WORKED 

Example 

15 

Mathcad 



1 William is to purchase a new video recorder. If William pays $125 monthly instalments 

over 3 years at an interest rate of 11.5% p.a. simple interest, what effective interest rate 

is he paying? 

2 

Item 

13F 

Cash 

price 

$ 

Deposit 

$ 

Monthly 

instalment 

$ 

For each of the items in the above table, calculate: 

i the total amount of interest charged on each item 

ii the total amount paid over the period given for each item 

iii the monthly instalment on each item 

iv the effective interest rate. 

Interest 

rate 

Term of 

loan 

a Television $875 $150 8% p.a. 2 years 

b New car $23 990 $2000 10% p.a. 5 years 

c Clothing $550 $100 7.5% p.a. 1 year 

d Refrigerator $1020 $50 6 -- 

% p.a. 18 months 

e Tools $250 $75 9% p.a. 15 months 

3 The cash price for a car is $4600. If the car is purchased on time payments the cost will 

be $5200. A deposit of $100 is required and the agreement is that the car will be fully 

paid for in 3 years, paid in equal monthly instalments. Find: 

a the monthly instalment 

b the simple (flat) interest rate per year 

c the effective interest rate. 

4 A camera valued at $1200 is purchased using a hire-purchase agreement. A deposit of 

$200 is required and equal monthly instalments of $75 are paid over the 18-month 

agreed period. Calculate: 

a the flat (simple) interest rate per annum 

b the effective interest rate. 

5 The bank approves a personal loan of $5000. A flat interest rate of 12.5% p.a. is 

charged, with repayments to be made over a 9-month period in equal weekly instalments. 

Calculate: 

a the weekly instalment 

b the effective interest rate. 

6 Calculate the effective interest rate on a loan of $1000 if the monthly repayments are 

$60 and the loan is to be repaid over 2 years. (Hint: First calculate the simple 

interest rate.) 

3 

4


7 Carefully read the advertisement (including the small print) for the purchase of the 

refrigerator below and calculate: 

a the flat interest rate 

b the effective interest rate 

c the total cost under the hire-purchase plan 

d the increase in cost over a cash sale. 

$599 

or 

$4.21 

weekly 

(one third deposit 

over two years) 

8 Copy and complete the following table. 

Cash 

price Deposit 

Instalment 

(monthly) Period 



rate 

$2500 $500 2 years 10% p.a. 

$150 $50 6 months 9.5% p.a. 

$685 $75 9 months 6 -- 

% p.a. 

$128 $ nil $11.20 1 year 

$6500 $500 $325 2 years 

Effective 


rate 

$10 000 $1500 5 years 10% p.a. 

3 

4 

WorkSHEET13.2





Effective 

rate of 



Spreadsheet applications 

Accountants, financial planners, banks and other financial institutions use spreadsheets 

to record and perform calculations. Many calculation tasks are similar in nature and 

tedious; therefore, once a spreadsheet is set up, some of these tasks can be done more 

quickly and easily. Another advantage of the use of a spreadsheet is solving the ‘what 

if’ question. This function allows the numbers entered on the spreadsheet to be changed 

and an answer to be calculated to predict what would happen in a particular scenario. 

This is particularly useful when looking at factors such as how much a person can 

borrow and pay back, changes in terms, and changes in interest rates. 

Your Maths Quest CD contains the Excel files ‘Simple interest’ and ‘Effective rate of 

interest’. These may be used to investigate various scenarios by typing new values in 

the yellow cells or by modifying the spreadsheet in some way. A screen shot of the file 

‘Simple Interest’ is shown below. 

Which is the best deal? 

1 Find three advertisements that offer products on hire purchase. 

2 Investigate each offer by calculating: 

a the total amount of interest to be paid 

b the total amount to be paid over the term of the loan 

c the monthly repayment 

d the effective interest rate. 

3 Compare this with other methods of financing the purchase of the product. 

4 Write a brief report on the advantages and disadvantages of each method.

summary 


Simple interest formula 

• A = P + I where A = Total amount ($) 

P = Principal or amount borrowed or invested ($) 

PrT 

• I = --------- 

100 




r = Rate of interest earned per period (% per period) 

T = Time, the number of periods over which the agreement operates 

• Interest rate, r, and time period, T, must be stated and calculated in the same time terms. 


• To find the principal 

100 × I 

P = ---------------r 

× T 

• To find the interest rate 

100 × I 

r = ---------------- 

P× T 

• To find the period of the loan or investment 

Bonds, debentures and term deposits 

100 × I 

T = ---------------- 

P× r 

• Term investments with governments are called bonds. 

• Term investments with companies are called debentures. 

• Term investments with banks are called term deposits. 

• All three are investments for a fixed period of time offering a simple interest rate. 

Savings banks — minimum monthly and daily balances 

• Two methods used by banks for calculating interest on savings accounts are: 

1. minimum monthly balances 2. daily balances. 

• Daily balances offer the best interest rate for investors. 

• Look at the balances on the first and last day of the month when establishing the 

minimum monthly balance or daily balances. 

1 

• Express days as a fraction of a year; for example, 1 day = -------- of a year. 

Hire-purchase 

• Hire-purchase is a loan for goods with interest calculated using flat rate (simple) 

interest and regular payments. 

• The main stages of calculations are: 

1. Loan amount = price of goods − deposit 

2. Flat rate interest on the loan is calculated using the simple interest formula. 

total amount 

Instalment amount = ---------------------------------------------------number 


Total cost of goods = deposit + loan amount + interest or 

= deposit + instalment amount × number of instalments 

Effective rates of interest 

• The effective interest rate is a true indication of the interest rate on a loan. It is 

calculated using a flat interest rate when the loan is progressively being reduced, 

such as in hire-purchases. 

1. Estimation: 

Effective interest rate is a little less than 2 × flat interest rate 

2. Calculation: 

2n 

Effective interest rate = ----------- 

× flat rate where n is the number of payments. 

n + 1 

365


CHAPTER review 

Multiple choice 

13A 1 

13A 

13A 

13B 

1 Two banks pay simple interest on short-term deposits. Bank A pays 6% p.a. over 4 years and 

Bank B pays 6.5% p.a. for 3 -- years. The difference between the two banks’ final payout 

2 

figure if $5000 was invested in each account is: 

A $0 B $1200 C $1137.50 D $150 E $62.50 

2 Clayton invested $360 in a bank for 3 years at 8% simple interest each year. At the end of 

the 3 years, the total amount he will receive is: 

A $86.40 B $236.80 C $28.80 D $388.80 E $446.40 

3 Philip borrowed $7000 and intended to pay it back in 4 years. The terms of the loan 

indicated Philip was to pay 9% p.a. interest. The interest Philip paid on the loan was: 

A $25 200 B $630 C $7630 D $9520 E $2520 

4 A loan of $5000 is taken over 5 years. The simple interest is calculated monthly. The 

interest bill on this loan is $1125. The simple interest rate per year on this loan is: 

1 

A 3% B 4 -- % C 3.75% D 5% E 3.5% 

13B, C 1 

13B 

13C 

13C 

13C 

2 

5 The principal invested in an investment bond that will accumulate $2015 after 6 months 

invested at 6 -- % p.a. is: 

2 

A $60 000 B $62 000 C $6200 D $50 000 E $5000 

6 A loan of $10 000 is taken over 10 years. The total interest bill on this loan is $2000. The 

simple interest rate per year on this loan is: 

1 

A 3% B 4 -- % C 2% D 5% E 2.5% 

1 

2 

2 

7 A 6-year bond pays 8 -- % p.a. simple interest. If Rhonda buys a bond worth $500, the 

interest she would earn would be: 

A $250 B $255 C $2550 D $233.75 E $230 

8 Simple interest was calculated on a term deposit of 5 years at 3 -- % p.a. When Leigh 

calculated her total return on her investment principal of $350, her return was: 

A $415.63 B $400 C $65.63 D $131.25 E $481.25 

3 

4 

9 State government bonds pay interest of 7 -- 

% p.a. simple interest. Jess invested $3500 in the 

bonds which mature in 5 years. Jess’s income each quarter would be: 

A $113.00 B $1356.25 C $3567.81 D $67.81 E $82.50 

3 

4

10 In the bank statement shown below the minimum balance for the month is: 


Date Transaction Deposit Withdrawal Balance 

5/4 Transfer from CBR $100 

$456.50 

7/4 Salary 

$1500 

$1956.50 

9/4 Cheque — 23456 

$1380 $576.50 

23/4 ATM — Rowville 

$125 $451.50 

A $456.50 B $1956.50 C $576.50 D $451.50 E $356.50 

11 A pearl necklace is purchased on hire-purchase for $225 deposit with equal monthly 

payments of $80 for 2 years. The cash price is $2000. The interest rate is: 

A 3.5% B 6% C 4% D 8% E 7.5% 

12 A hire-purchase contract specifies that there are to be monthly payments for 2 years. The 

flat rate of interest is 6.3% p.a. The effective interest rate for this contract is closest to: 

A 12.1% B 11.6% C 8.4% D 6.3% E 12.6% 

Short answer 

1 Cynthia invested $270 with a building society in a fixed deposit account that paid 8% p.a. 

simple interest for 4 years. How much did Cynthia receive at the end of the 4 years? 

2 A bank offers 8.5% p.a. simple interest on an investment. At the end of 3 years the interest 

earned was $765. How much was invested? 

3 If $725 is invested for 3 years and earns $206.65 interest, calculate the yearly interest rate. 

1 

4 Jack put some money away for 4 -- years in a bank account which is paying 3 -- % p.a. 

2 

4 

interest. He found on his bank statement he had earned $67.50. How much did Jack invest? 

5 Jacob needed to earn $225 in one year. He invested $2000 in an account earning simple 

interest at a rate of 4.5% p.a. paid monthly. How many months will it take Jacob to achieve 

his aim? 

3 

13D 

13E 

13F 

13A 

13B 

13B 

13B 

13B

13C 

13C 

13C 


6 Steve invested the $1800 he won at the races in an insurance company bond that pays 12 -- % 

2 

p.a. provided he keeps the bond for 4 years. What is Steve’s total return from the bond at the 

end of the 4 years? 

7 Jocelyn buys $3500 worth of debentures in a company. She earns 8.5% p.a. simple interest 

paid to her quarterly. If the agreed period of the debenture was 28 months, calculate the 

amount of interest Jocelyn will earn. 

8 The bank offers a term deposit account paying investors 10.5% p.a. on investments over 

$10 000 for 2 years. Paul decides to invest $12 000 in this account. How much interest will 

he earn at the end of the investment? 

13C 1 

13D 

13D 

9 An investment bond is offered to the public at 10% per year. Louis buys a bond worth $4000 

1 

that will mature in 2 -- years. How much in total will Louis receive at the end of the 2 -- years? 

10 At the beginning of July, Ross had $580 in his savings bank account. On 15 July he 

withdrew $80. If the bank pays 8% p.a. interest paid monthly, calculate the interest Ross 

earns in July: 

a if calculated on the minimum monthly balance 

b if calculated on the daily balance. 

11 


1/5 

3/5 

7/5 

19/5 

27/5 

2 

$12 

$6 

$28.80 

Deborah’s passbook shows the above transactions for May. Calculate the interest Deborah 

3 

will earn in May if the bank pays 4 -- 

% p.a. simple interest monthly: 

4 

a on the minimum monthly balance 

b on the daily balance. 

$10 

2 

$302.20 

$273.40 

1

12 The cash price of a car is $18 000. 

If a customer pays a deposit of $3000 

and pays equal monthly instalments 

of $300 over 5 years, calculate: 

a the amount of interest charged 

b the flat rate of interest 

c the total paid for the car 

d the effective interest rate. 


13 The cash price for a bicycle is $460. If the bike is purchased on time payments the total cost 

will be $550. A deposit of $50 is required and the agreement is that the bike will be fully 

paid for in 2 years, in equal monthly instalments. Find: 

a the monthly instalment 

(round up to the nearest cent) 

b the simple interest rate per year 

(to 1 decimal place) 

c the effective interest rate 

(to 1 decimal place). 

13E, F 

13E, F

test 

yourself 

ourself 

CHAPTER 

13 


Analysis 

1 

Date Description Debit Credit Balance 

4 August 

8 August 

19 August 

27 August 

28 August 

ATM 

Deposit 

EFTPOS 

Salary 

ATM 

100.00 

119.50 

1527.40 

325.60 

975.60 

2383.50 

1983.50 

a Complete the missing credits, debits and balances in the shaded areas of the above account. 

b The bank is offering 2.4% p.a. on the minimum monthly balance. What is the interest rate 

per month? 

c Calculate the interest that was earned for the month of August. 

2 Geoff wants to buy a windsurfer. Its retail price is $3995. Geoff’s first option for financing the 

purchase is using hire-purchase. The terms offered by Your Money Finance Company is 

10% deposit with fortnightly instalments over 2 years at an interest rate of 7.8% per annum. 

a How much will Geoff need to withdraw from his savings account to pay the deposit? 

b Calculate the fortnightly repayments and total interest charge. 

c What is the total cost of the windsurfer? 

d A personal loan is advertised at 13.5% per annum. For Geoff to compare the interest rate 

he needs to convert the hire-purchase flat rate of interest to the effective interest rate. 

Calculate the effective interest rate. 

3 Another option is for Geoff to save up until he has the cash to pay for the windsurfer. He can 

place the balance of his savings account (shown above in question 1) into a term deposit 

offering 5.6% per annum for a 2-year term. 

a Calculate the total value of his investment at the end of 2 years. 

b Geoff uses the term deposit investment towards the purchase of the windsurfer. What extra 

fortnightly savings will be needed over the next 2 years to make up the balance of $3995? 

c What is the main attraction of the hire-purchase option over the options in 3a and b?

Simple interest

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