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VCE 11 General 2023

4.07 Compound interest

Worksheet
Compound interest tables
1

\$3900 is invested for three years at a rate of 10\% p.a., compounded annually.

a

Complete the table below to determine the final value of the investment:

Balance at beginning of yearInterest earned
First year\$3900\$390
Second year\$4290\$429
Third year
Fourth year-
b

Calculate the total interest earned over the three years.

2

\$3700 is invested for three years at a rate of 7\% p.a., compounded annually.

a

Complete the table below to determine the final value of the investment:

Balance at beginning of yearInterest earned
First year\$3700\$259
Second year\$3959\$277.13
Third year
Fourth year-
b

Calculate the total interest earned over the three years.

3

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

Time Period (years)Value at beginning of time periodValue at end of time periodInterest earned in time period
1\$3000AB
2C\$3244.80D
3\$3244.80\$3374.59E
a

Find the value of:

i
A
ii
B
iii
C
iv
D
v
E
b

Calculate the total interest earned over the three years.

4

\$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 three years.

c

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

Interest ($)Balance ($)
Starting balance09000
After one year
After two years
After three years
5

Maria invested \$1400 at 10\% p.a., compounded annually over 3 years. Without using the compound interest formula calculate:

a

The interest earned for the first year.

b

The balance after the first year.

c

The interest earned for the second year.

d

The balance after the second year.

e

The interest earned for the third year.

f

The balance after the third year.

g

The total amount of interest earned over the three years.

h

The interest as a percentage of the initial investment, correct to one decimal place.

i

The interest earned after three years if the investment was simple interest rather than compound interest.

j

Which type of interest is best for this investment and by how much is it better.

6

The following compound interest table shows the final value of a \$1000 investment, for various interest rates, compounded annually over various numbers of years:

5 \text{ years}10 \text{ years}15 \text{ years}20 \text{ years}25 \text{ years}
r = 5\% \text{ p.a.}1628.891790.851967.152158.922367.36
r = 6\% \text{ p.a.}2078.932396.562759.033172.173642.48
r = 7\% \text{ p.a.}2653.303207.143869.684660.965604.41
r = 8\% \text{ p.a.}3386.354291.875427.436848.488623.08
r = 9\% \text{ p.a.}4321.945743.497612.2610\,062.6613\,267.68

If \$50\,000 is invested and earns interest at 6\% p.a. over 15 years, calculate:

a

The value of this investment.

b

The amount of interest earned.

7

The following compound interest table shows the final value of a \$1 investment, for various interest rates, compounded annually over various numbers of years:

10 \text{ years}11 \text{ years}12 \text{ years}13 \text{ years}14 \text{ years}15 \text{ years}
r = 8\%2.15892.33162.51822.71962.93723.1722
r = 9\%2.36742.58042.81273.06583.34173.6425
r = 10\%2.59372.85313.13843.45233.79754.1772
r = 11\%2.83943.15183.49853.88334.31044.7846
r = 12\%3.10583.47853.8964.36354.88715.4736

After how many years will a sum of money triple in value if it is invested at 10\% p.a., compounded annually?

Compound interest formula
8

Find the future value of the following:

a

An investment of \$2000 earns interest at 6\% p.a, compounded annually over 4 years.

b

An investment of \$1000 earns interest at 2\% p.a., compounded semiannually over 3 years.

c

An investment of \$8030 earns interest at 3\% p.a., compounded annually over 20 years.

d

An investment of \$4490 earns interest at 2.8\% p.a., compounded semiannually over 6 years.

e

An investment of \$8030 earns interest at 3\% p.a., compounded quarterly over 12 years.

f

An investment of \$9450 earns interest at 2.6\% p.a., compounded monthly over 14 years.

g

An investment of \$1710 earns interest at 2.2\% p.a., compounded weekly over 6 years.

h

An investment of \$3000 earns interest at 4.5\% p.a., compounded daily over 5 years. Assume one leap year over this period.

i

An investment of \$392 earns interest at 2\% p.a., compounded annually for 7 years. After this time the principal plus interest is reinvested at 4\% p.a., compounded annually for 5 more years.

9

Maria has \$1000 to invest for 4 years and would like to know which of three investment plans to choose:

  • Plan 1: invest at 4.98\% p.a. interest, compounded monthly.

  • Plan 2: invest at 6.44\% p.a. interest, compounded quarterly.

  • Plan 3: invest at 5.70\% p.a. interest, compounded annually.

a

Calculate the future value of each investment plan.

b

State which plan Maria should choose for maximum return on her investment.

10

Hannah put \$600 in a savings account with interest compounded quarterly at a rate of \\ 1.1\% p.a. Calculate the amount that is in Hannah's account after a period of 21 months.

11

Tina has \$900 in a savings account which earns compound interest at a rate of 2.4\% p.a.

If interest is compounded monthly, how much interest does Tina earn in 17 months?

12

John borrows \$6000 from a loan shark at a rate of 20\% p.a. compounded annually. If he is not able to make any repayments, calculate how much John will owe at the end of 5 years.

13

Emma borrows \$7000 from a loan shark at a rate of 4.7\% p.a. compounded annually. If she is not able to make any repayments, calculate how much Emma will owe at the end of 3 years.

Calculate the principal
14

Scott wants to have \$1500 at the end of 5 years. If the bank offers 2.3\% p.a. compounded annually, how much should he invest now?

15

Tom wants to put a deposit on a house in 4 years time. In order to finance the \$12\,000 deposit, he decides to put some money into a high interest savings account that pays \\ 5\% p.a. interest, compounded monthly. If P is the amount of money that he must put into his account now to accumulate enough for the deposit, find P.

16

Ursula has just won \$30\,000. She decides to invest some of her winnings into a retirement fund which earns 8\% interest p.a., compounded yearly. When she retires in 29 years, she wants to have \$52\,000 in her fund.

How much of her winnings should Ursula invest now to achieve this?

17

Beth's investment into a 12-year 4.4\% p.a. corporate bond grew to \$13\,190.

Calculate the size of Beth's initial investment if the interest was compounded:

a

Annually

b

Semiannually

c

Quarterly

d

Monthly

e

Weekly

f

Daily

18

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?

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