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2.01 Simple interest formula

Worksheet
Simple interest
1

Calculate the simple interest charged on a loan of \$2600 at 8\% p.a. for 4 years.

2

Calculate the simple interest earned on an investment of \$8760 at 2\% p.a. for 7 years.

3

Luke's investment of \$9000 earned simple interest of 10\% p.a. for the first 4 years and 3\% p.a. for the next 7 years.

a

Calculate the total amount of interest he earned.

b

Calculate the final value of his investment.

4

Elena invests \$303 at 2\% p.a. simple interest for 7 years.

After this time she reinvests the principal plus interest at 6\% p.a. simple interest for 5 more years.

a

What is the value of her investment after 7 years?

b

What is the final value of her investment?

c

How much interest did she earn in total?

5

Beth takes out a car loan of \$3000 at a simple interest rate of 8\% p.a.

She plans to repay the loan over 4 years through equal regular monthly repayments.

a

Calculate the total interest that Beth will be charged over the duration of the loan.

b

Calculate the value of each loan repayment.

6

Dave and Maggie are looking to invest \$7900 and \$20\,600 respectively for 9 years. This table shows the simple interest offered for different principals.

a

How much interest will Dave earn on his investment?

b

How much interest will Maggie earn on her investment?

c

How much will they earn if they invest their money together?

d

How much more interest will they earn by combining their money?

PrincipalRate p.a.
\text{Between }\$4600\text{ and }\$14\,6003\%
\text{Between }\$14\,600\text{ and }\$24\,6004\%
\text{Greater than }\$24\,6005\%
7

Calculate the simple interest earned on the following investments. Assume that a year has 52 weeks or 365 days.

a

\$5370 at 10\% p.a. for 3 years.

b

\$4640 at 2\% p.a. for 23 months.

c

\$3180 at 3\% p.a. for 31 months.

d

\$7530 at 4\% p.a. for 16 months.

e

\$5320 at 3\% p.a. for 77 weeks.

f

\$5150 at 9\% p.a. for 37 weeks.

g

\$7580 at 10\% p.a. for 84 weeks.

h

\$6680 at 6\% p.a. for 678 days.

i

\$4370 at 7\% p.a. for 200 days.

j

\$400 invested at 9\% p.a. for 3 months.

k

\$8310 invested at 1.8\% per half-year for 2 years.

l

\$5450 invested at 7\% p.a. for 569 days.

m

\$5000 invested at 1.7\% per quarter for 9 years.

8

If \$16\,716 of simple interest was earned in 7 years, find how much interest was earned each:

a

year

b

month

9

Calculate the simple interest on a loan of \$8000 at 8\% p.a. for 6 years. Round your answer to the nearest dollar.

10

Ned borrowed \$3600 from a bank at a simple interest rate of 2.5\% for one year.

a

How much interest will Ned need to pay after one year?

b

What is the total amount Ned will have to repay the bank at the end of 1 year?

11

What is the total interest to be paid on a 3-year \$8000 loan at 13\% p.a. flat interest?

12

Buzz takes out 6-year \$50\,000 loan at 8\% p.a. flat interest.

a

What is the total interest he will have to pay?

b

What is the total amount he will have to pay?

13

What is the total amount to be paid on a 5-year loan of \$110\,000 at 5\% p.a. flat interest?

14

Sally pays for her purchase of a new carpet, valued at \$9000, by paying a \$3000 deposit and borrowing the balance at 5\% p.a. flat interest to be repaid over 3 years.

a

What is the total interest she will have to pay?

b

What is the total amount she will pay for the carpet?

Interest rate
15

Amelia made loan repayments totalling to \$1360 on a loan of \$1000 over 6 years.

a

Calculate the total simple interest charged on the loan.

b

Calculate the percentage annual simple interest rate.

16

For each of the following investments find the annual interest rate, r, as a percentage rounded to one decimal place.

a

\$2220 invested over 8 years earns \$728.16 in interest.

b

\$1040 invested over 5 years earns \$442.00 in interest.

c

\$7500 invested over 10 quarters earns \$1781.25 in interest.

d

\$9300 invested over 9 quarters earns \$585.90 in interest.

e

\$6600 invested over 20 months earns \$528.00 in interest.

f

\$3400 invested over 14 months earns \$170.57 in interest.

17

If \$2196 is invested at 2\% p.a. simple interest for 8 years, what simple interest rate, r, would earn the same amount of interest in only 5 years?

18

The simple interest on an investment of \$3600 over 2 years is \$504.00. Find the annual interest rate to one decimal place.

19

The graph shows the amount of simple interest charged each year by a particular bank, on a 3-year loan.

a

Find the total amount of simple interest charged on a loan of \$5000.

b

Calculate the simple interest rate per annum charged by the bank on 3-year loans.

1000
2000
3000
4000
P
50
100
150
200
250
300
I
20

The given graph shows an amount of \$4000 deposited into a savings account for 10 years earning simple interest.

a

How much interest has been earned in total over the 10 year period?

b

Find the interest rate to two decimal places.

1
2
3
4
5
6
7
8
9
10
T
3250
3500
3750
4000
4250
4500
4750
A
Duration
21

Dave invests \$635 at 5\% p.a simple interest. He wants to know the number of years it will take the investment to grow to \$889.00.

a

Calculate the interest that must be earned on the investment for Dave to reach his goal.

b

Hence calculate the number of whole years it will take for the investment to reach his goal.

22

For how many years does \$4750 need to be invested for it to grow to \$4940, if simple interest is paid at 8\% p.a.? Round your answer to two decimal places.

23

For how many whole years does \$4078 need to be invested to earn \$4078 in interest, if simple interest is paid at 10\% p.a.?

24

For how many whole months does \$49\,610 need to be invested to earn \$6697.35 in interest, if simple interest is paid at 9\% p.a.?

25

For how many whole quarters does \$7151.00 need to be invested to earn \$250.29 in interest, if simple interest is paid at a rate of 2\% p.a.?

Principal
26

Calculate the amount of money that was originally invested at 8\% p.a. and earned \$340 simple interest over 2 years.

27

Find the principal that earned \$520 simple interest over 6 months at a rate of 4\% per annum.

28

Find the principal that earned:

a
\$865 simple interest, at 3\% p.a. over 6 years.
b
\$390 simple interest, at 2.5\% p.a. over 4 years.
c
\$1200 simple interest, at 1\% per month over 2 years.
d
\$3260 simple interest, at 2.5\% per week over 6 months.
29

For his investment into government bonds , Buzz was paid simple interest of 6\% p.a. Calculate the size of Buzz's initial investment \$P if he earned \$1094.40 interest after 10 years.

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Outcomes

ACMGM006

apply percentage increase or decrease in various contexts; for example, determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest

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