topic badge

2.03 Other compounding periods

Worksheet
Final value
1

Calculate the final value of the following investments:

a
A \$5800 investment earns interest at 4\% p.a. compounded quarterly over 17 years.
b
A \$9090 investment earns interest at 4.7\% p.a. compounded half-yearly over 11 years.
c
A \$8920 investment earns interest at 3.3\% p.a. compounded monthly over 5 years.
d
A \$3420 investment earns interest at 4.9\% p.a. compounded weekly over 9 years. Assume 52 weeks in a year.
e
A \$6000 investment earns interest at 5\% p.a. compounded daily over 11 years. Assume 365 days in a year.
2

Calculate the final value of the following investments:

a
\$4000 is invested in a term deposit at a rate of 3\% per quarter compounded monthly for 8 years.
b
\$3000 is invested in a term deposit at a rate of 1\% per month compounded quarterly for 6 years.
3

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

a
Brad borrows \$8000 from a loan shark at a rate of 5.4\% p.a. compounded semi-annually, for 5 years.
b
Victoria borrows \$4000 from a loan shark at a rate of 2.8\% p.a. compounded quarterly, for 3 years.
c
\$6000 is borrowed from a bank at a rate of 7.2\% p.a. compounded weekly, for 5 years.
d
\$7000 is borrowed from a bank at a rate of 3.4\% p.a. compounded monthly, for 6 years.
e
\$2000 is borrowed from a bank at a rate of 1.3\% p.a. compounded daily, for 3 years. Assume there are 365 days in a year.
4

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

a

Calculate the value of the investment if it is compounded quarterly.

b

Calculate the value of the investment if it is compounded monthly.

c

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

5

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

Which investment plan yields the highest return?

6

\$5000 is deposited into an account that attracts interest at a rate of 3.4\% per annum. Find how much is in the account after 8 years if:

a

Interest is compounded annually.

b

Interest is compounded monthly.

c

Simple interest is used instead of compound interest.

7

Show that it is financially better to invest an amount of money at a rate of 5\% p.a. compound interest, rather than at a rate of 5\% p.a. simple interest.

Interest
8

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

9

Calculate the amount of interest earned on the following investments:

a
Sarah'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 half-yearly over 2 years.
10

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

11

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.

12

Jenny applies for a loan of \$9000 over 3 years and she is offered the choice between two loan rates:

  • Rate 1: Simple interest at a rate of 3\% p.a.

  • Rate 2: Compound interest at a rate of 2.5\% p.a. compounded daily.

a

How much simple interest would she pay if she chose the first loan?

b

How much compound interest would she pay if she chose the second loan? Assume there are 365 days in a year.

c

Which rate should Jenny choose? Explain your answer.

13

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?

Principal
14

After 8 years, Ally's investment is worth \$24\,900. Her investment grew at a rate of 12\% p.a. compounded monthly. How much money did Ally initially invest?

15

After 11 years, Kyle paid back his loan which had acuumulated to \$36\,840. His loan had an interest rate of 12\% p.a. compounded quarterly. How much money did Kyle initially borrow?

16

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.

17

Carl is expecting a Christmas bonus of \$1800 in 4 months time. What is the most he can borrow now, at a rate of 4.1\% p.a. compounded daily, and still be able to pay off the loan with his bonus?

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