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7.02 Compound interest

Worksheet
Compound interest
1

Describe how compound interest is earned.

2

\$9000 is invested for 3 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}
3

\$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.

4

A \$7510 investment earns interest at 4.5\% p.a. compounded annually over 6 years.

a

For the compound interest formula A=P(1+i)^n, state the value of:

i
P
ii
i
iii
n
b

Calculate the value of A.

5

A \$3400 investment earns interest at 3\% p.a. compounded quarterly over 19 years.

a

For the compound interest formula A=P(1+i)^n, find the value of:

i
P
ii
i
iii
n
b

Calculate the value of A.

6

A \$9090 investment earns interest at 4.7\% p.a. compounded semiannually over 11 years.

a

For the compound interest formula A=P(1+i)^n, find the value of:

i
P
ii
i
iii
n
b

Calculate the value of A.

7

A \$8920 investment earns interest at 3.3\% p.a. compounded monthly over 5 years.

a

For the compound interest formula A=P(1+i)^n, find the value of:

i
P
ii
i
iii
n
b

Calculate the value of A.

8

A \$3420 investment earns interest at 2.6\% p.a. compounded weekly over 9 years. Assume there are 52 weeks in one year.

a

For the compound interest formula A=P(1+i)^n, find the value of:

i
P
ii
i
iii
n
b

Calculate the value of A.

9

A \$6000 investment earns interest at 7.3\% p.a. compounded daily over 11 years. Assume there are 365 days in one year.

a

For the compound interest formula A=P(1+i)^n, find the value of:

i
P
ii
i
iii
n
b

Calculate the value of A.

10

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?

11

Calculate the amount, A, that an investment of \$1000 compounded annually is worth after:

a

3 years at an interest rate of 4\% p.a.

b

4 years at an interest rate of 9\% p.a.

12

\$4000 is invested in a term deposit at a rate of 3\% per quarter compounded monthly. Find the value of the investment after 8 years.

13

\$3000 is invested in a term deposit at a rate of 1\% per month compounded quarterly. Find the value of the investment after 6 years.

14

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?

15

\$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?

16

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

17

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?

18

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?

19

Calculate how much is owed at the end of the following loan periods:

a

\$6000 is borrowed at a rate of 20\% p.a. compounded annually for 5 years.

b

Emma borrows \$7000 at a rate of 4.7\% p.a. compounded annually for 3 years.

20

\$8000 is borrowed at a rate of 5.4\% p.a. compounded semi-annually for 5 years.

a

For the compound interest formula A=P(1+i)^n, state the value of:

i
P
ii
i
iii
n
b

Calculate the final value of the loan A.

c

Calculate the interest owed on the loan I.

21

Assuming that a year has 52 weeks and 365 days, calculate how much is owed at the end of the following loan periods, given that no repayments are made:

a

\$4000 is borrowed at a rate of 2.8\% p.a. compounded quarterly for 3 years.

b

\$6000 is borrowed from a bank at a rate of 7.2\% p.a. compounded weekly for 5 years.

c

\$7000 is borrowed from a bank at a rate of 3.4\% p.a. compounded monthly for 6 years.

d

\$2000 is borrowed from a bank at a rate of 1.3\% p.a. compounded daily for 3 years.

22

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?

23

Sean borrows \$7000 at a rate of 5.5\% p.a. compounded weekly. If she pays off the loan in a lump sum at the end of 5 years, find how much interest she pays. Assume there are 52 weeks in a year.

24

Assuming that in a year there are 52 weeks and 365 days, calculate the amount of interest earned on the following investments:

a

Sally's investment of \$4200 earns interest at 2.7\% p.a. compounded quarterly over 13 years.

b

Sally's investment of \$3070 earns interest at 4.5\% p.a. compounded monthly over 7 years.

c

Han's investment of \$9110 earns interest at 3.2\% p.a. compounded weekly over 18 years.

d

Luke's investment of \$6220 earns interest at 2.8\% p.a. compounded daily over 11 years.

e

Buzz's investment of \$4920 earns interest at 5\% p.a. compounded semiannually over 2 years.

f

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

25

Pauline borrows \$50\,000 at a rate of 5.4\% per annum. If she pays off the loan in a lump sum at the end of 7 years, find how much interest she pays if the interest is compounded:

a

Daily

b

Monthly

c

Quarterly

26

Emma wants to invest \$1400 at 5\% p.a for 5 years. She has two investment options, compounding quarterly or compounding monthly.

Calculate how much extra the investment is worth if it is compounded monthly rather than quarterly.

27

Maria has \$9000 to invest for 5 years and would like to know which investment plan to enter into out of the following three.

  • Plan 1: invest at 4.51\% p.a. interest, compounded monthly

  • Plan 2: invest at 6.16\% p.a. interest, compounded quarterly

  • Plan 3: invest at 5.50\% p.a. interest, compounded annually

Find the difference in investment return if Maria chooses the worst plan, compared to the best plan.

28

Mae's investment into a 20-year 2.33\% p.a. corporate bond grew to \$13\,600. Calculate the size of Mae's initial investment if interest was compounded:

a

Annually

b

Half-yearly

c

Quarterly

d

Monthly

e

Weekly, assuming there are 52 weeks in a year.

f

Daily, assuming there are 365 days in a year.

29

Katrina borrows \$6500 at a rate of 6.6\% p.a. compounded semi-annually. If she pays off the loan in a lump sum at the end of 5 years, find how much interest she pays.

30

Frank is working out the compound interest accumulated on his loan. He writes down the following working:

A = 6000\left(1+\dfrac{0.08}{4}\right)^{(7\times4)}

a

How much did he borrow in dollars?

b

What is the annual interest rate as a percentage?

c

Is the interest being compounded weekly, monthly, quarterly or annually?

d

For how many years is he accumulating interest?

e

How much interest does he pay?

Spreadsheets
31

The following spreadsheet shows the balance in a savings account where interest is compounded quarterly:

ABCD
1\text{Quarter}\text{Balance at the beginning} \\ \text{of quarter}\text{Interest}\text{Balance at the end} \\ \text{of quarter}
21\$100\$5100
32\$5100\$5202.00
43\$5202.00\$104.04
54\$5306.04\$106.12\$5412.16
a

Calculate the quarterly interest rate, correct to two decimal places.

b

Complete the table.

32

The following spreadsheet shows the balance in a savings account, where interest is compounded monthly:

ABCD
1\text{Month}\text{Balance at the beginning} \\ \text{of month}\text{Interest}\text{Balance at the end} \\ \text{of month}
2\text{July}\$3000\$30\$X
3\text{August}\$3030\$30.30\$3060.30
4\text{September}\$3060.30\$Y\$3090.90
5\text{October}\$Z\$30.91\$3121.81
6\text{November}\$3121.21\$31.22\$3153.03

Complete the table.

33

The following spreadsheet shows the balance in a savings account, where interest is compounded monthly:

ABCD
1\text{Month}\text{Balance at the beginning} \\ \text{of month}\text{Interest}\text{Balance at the end} \\ \text{of month}
2\text{January}\$1000\$20\$1020
3\text{February}\$1020\$20.40\$1040.40
4\text{March}\$1040.40\$20.81\$1061.21
5\text{April}\$1061.21\$21.22\$1082.43
6\text{May}
a

Use the numbers for January to calculate the monthly interest rate.

b

Complete the table for the month of May.

c

Use a spreadsheet to calculate the total amount of interest earned over the year.

34

The following spreadsheet shows the balance in a savings account in 2019, where interest is compounded quarterly:

ABCD
1\text{Quarter}\text{Balance at the beginning} \\ \text{of quarter}\text{Interest}\text{Balance at the end} \\ \text{of quarter}
21\$2000\$20\$2020
32\$2020\$20.20\$2040.20
43\$2040.20\$20.40\$2060.60
54
a

Calculate the quarterly interest rate.

b

Complete the table for quarter 4.

c

Use a spreadsheet to find how many quarters after the beginning of 2019 the balance will be double the initial investment of \$2000.

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Outcomes

4.3.1.2

understand the concept of compound interest as a recurrence relation

4.3.1.4

use technology (online calculator) to calculate the future value of a compound interest loan or investment and the total interest paid or earned

4.3.1.5

use technology (spreadsheet) to calculate the future value of a compound interest loan or investment and the total interest paid or earned [complex]

4.3.1.8

use technology (online calculator) to investigate the effect of the interest rate and the number of compounding periods on the future value of a loan or investment

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