topic badge

2.02 Compound interest

Worksheet
Compound interest tables
1

\$9000 is invested for three years at a rate of 5\% p.a. compounded annually.

a

Complete the table:

b

Calculate the total interest accumulated over 3 years.

c

Calculate the value of the investment at the end of 3 years.

\text{Interest } (\$)\text{Balance } (\$)
\text{After } 0 \text{ years}09000
\text{After } 1 \text{ year}
\text{After } 2 \text{ years}
\text{After } 3 \text{ years}
2

\$3000 is invested at 4\% p.a., compounded annually. The table below tracks the growth of the principal over three years.

\text{Value at start of time period }\text{Value at end of time period }\text{Interest earned }
1st year\$3000AB
2nd yearC\$3244.80D
3rd year\$3244.80\$3374.59E
a

Find the value of:

i
A
ii
B
iii
C
iv
D
v
E
b

Find the total interest earned over the three years.

Compound interest formula
3

Describe how compound interest is earned.

4

Use the compound interest formula to calculate the amount, A, that an investment of \$1000 is worth after 3 years at an interest rate of 4\% p.a. compounded annually.

5

Use the compound interest formula to calculate the amount, A, that is owed after 4 years if

\$1000 is borrowed at an interest rate of 9\% p.a. compounding annually.

6

A \$7510 investment earns interest at 4.5\% p.a. compounded annually over 6 years. Use the compound interest formula to calculate the final value of this investment.

7

Joan's investment of \$3000 earns interest at a rate of 3\% p.a, compounded annually over 4 years. What is the value of the investment at the end of the 4 years?

8

John borrows \$6000 from a loan shark at a rate of 20\% p.a. compounded annually. He is not able to make any repayments for 5 years. How much does he owe at the end of 5 years?

9

Emma borrows \$7000 from a loan shark at a rate of 4.7\% p.a. compounded annually. She is not able to make any repayments for 3 years. How much does she owe at the end of 3 years?

10

\$380 is invested at 2\% p.a. compounded annually for 5 years. At the end of 5 years, the entire value of the investment is reinvested at 3\% p.a. compounded annually for 4 more years. What is the final value of the investment at the end of the 9 years?

11

Kate invests \$3000 at a rate of 2\% p.a. compounded annually. Find how much the investment is worth after:

a

24 months

b

18 months

c

30 months

12

Ben borrows \$7000 at a rate of 2\% p.a. compounded annually. After 2 years he makes a repayment of \$500. After another 3 years, with no further repayments, how much does Ben owe?

13

Xavier invests \$7000 in a term deposit with a rate of 2\% p.a. compounded annually. After 3 years he withdraws \$600, and leaves the rest in the the term deposit for 2 more years. How much is the investment worth after the total 5 years?

Compound interest
14

\$4000 is deposited into an account that attracts interest at a rate of 2.5\% per annum. Find the amount of interest accumulated over 8 years if:

a

Simple interest is used.

b

The interest is compounded annually.

15

Amelia borrows \$2400 at a rate of 6.3\% p.a. compounded annually. If she pays off the loan in a lump sum at the end of 5 years, how much interest does she pay?

16

Sally's investment of \$8910 earns interest at 4\% p.a. compounded annually over 10 years.

How much interest was earned during this period?

17

Lachlan borrows \$5000 at a rate of 4.5\% compounded annually. After 2 years the bank increases the interest rate to 4.6\%. If he pays off the loan in a lump sum at the end of 5 years, how much interest does he pay?

18

Bob applies for a loan of \$5000 over 4 years at a rate of 3.5\% per annum. He is offered the choice between simple interest and interest compounded annually.

a
Calculate how much interest he would he pay if he chooses:
i
Simple interest
ii
Compound interest
b
Which type of interest should he choose in order to minimise the amount of interest he has to pay?
Principal
19

Over 6 years, an investment accumulated to \$84\,000. If the compound interest rate was 4.6\% p.a. for the entire 6 years, calculate the original amount invested.

20

Alex borrowed money from the bank for 4 years at a rate of 7.5\% per annum. At the end of the 4 years he owed the bank \$8950. How much did he initially borrow?

21

Jeremy has just won \$50\,000. When he retires in 15 years, he wants to have \$94\,000 in his fund which earns 6\% interest per annum. How much of his winnings does he need to invest now to achieve this?

22

Victoria has been promised an inheritance of \$70\,000 in 5 years time. What is the most she can borrow now at a rate of 7\% p.a. compounded annually, and still be able to pay off the loan with her inheritance?

Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

1.1.1.6

apply percentage increase or decrease in various contexts, e.g. 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

What is Mathspace

About Mathspace