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Stage 5.1

7.06 Visualising compound interest

Worksheet
Compound interest graphs
1

State whether the following graphs could represent a savings account that earns compound interest over 50 years:

a
\text{Time (years)}
\text{Balance} \left(\$\right)
b
\text{Time (years)}
\text{Balance} \left(\$\right)
c
\text{Time (years)}
\text{Balance} \left(\$\right)
d
\text{Time (years)}
\text{Balance} \left(\$\right)
2

Consider the following graph showing two investments, one with simple interest (Investment A) and another with compound interest (Investment B):

a

Which investment has a higher principal amount?

b

Which investment has a higher final amount after 10 years?

c

After how many years will the investments be equal in value?

1
2
3
4
5
6
7
8
9
10
11
\text{Time (years)}
2
4
6
8
10
\text{Investment } \left(\$1000\right)
3

\$1000 is invested for 10 years with an interest rate of 10\% per annum that includes the accumulated interest.

a

Is this an example of simple or compound interest? Explain your answer.

b

Sketch a graph showing the growth of the investment.

4

Paul used repeated applications of simple interest to calculate how much an investment of \$2000 would grow over 3 years if it earned compound interest at a rate of 22\% p.a., compounded annually:

YearBalance + interestValueInterest earned
\text{Start of investment, } 0\qquad \quad \enspace -\quad \quad \$ 2000.00\qquad \$440
\text{First year, } 1\quad \$ 2000.00 + \$440.00\qquad \$ 2440.00\qquad \$ 536.80
\text{Second year, } 2\quad \$ 2440.00 \, + \$ 536.80\qquad \$ 2976.80\qquad \$654.90
\text{Third year, }3\quad \$ 2976.80 + \$654.90\qquad \$ 3631.70\qquad\quad -
a

Plot the relationship between the number of years passed and the value of the investment.

b

Is the growth of the investment linear or non-linear?

5

Amy used repeated applications of simple interest to calculate how much an investment of \$300 would grow over 3 years if it earned compound interest at a rate of 23\% p.a., compounded annually:

YearBalance + interestValueInterest earned
\text{Start of investment, }0\qquad \quad \enspace -\quad \quad \$ 300.00\qquad \$69.00
\text{First year, }1\quad \$ 300.00 + \$ 69.00\qquad \$ 369.00\qquad \$ 84.87
\text{Second year, }2\quad \$ 369.00 \, + \$ 84.87\qquad \$ 453.87\qquad \$104.39
\text{Third year, }3\quad \$ 453.87 + \$104.39\qquad \$ 558.26\qquad\quad -
a

Plot the relationship between the number of years passed and the value of the investment.

b

Is the growth of the investment linear or non-linear?

6

William used repeated applications of simple interest to calculate how much an investment of \$400 would grow over 3 years if it earned interest at a flat rate of 6\% p.a., compounded annually:

YearBalance + interestValueInterest earned
\text{Start of investment, }0\qquad \quad \enspace -\quad \quad \$ 400.00\qquad \$24.00
\text{First year, }1\quad \$ 400.00 + \$ 24.00\qquad \$ 424.00\qquad \$ 24.00
\text{Second year, }2\quad \$ 424.00 \, + \$ 24.00\qquad \$ 448.00\qquad \$24.00
\text{Third year, }3\quad \$ 448.00 + \$24.00 \qquad \$ 472.00\qquad\quad -
a

Plot the relationship between the number of years passed and the value of the investment.

b

Is the growth of the investment linear or non-linear?

7

Sharon used repeated applications of simple interest to calculate how the value of a boat currently valued at \$500 would decrease over 3 years if it depreciated at a rate of 26\% per year:

YearBalance + interestValueDepreciation
\text{Current value, }0\qquad \quad \enspace -\quad \quad \$ 500.00\qquad \$130.00
\text{First year, }1\quad \$ 500.00 - \$ 130.00\qquad \$ 370.00\qquad \$ 96.20
\text{Second year, }2\quad \$ 370.00 \, - \$ 96.20\qquad \$ 273.80\qquad \$71.19
\text{Third year}\quad \$ 273.80 - \$71.19 \qquad \$ 202.61\qquad\quad -
a

Plot the relationship between the number of years passed and the value of the boat.

b

Is the depreciation of the boat's value linear or non-linear?

8

Luke invests \$50 into an account which accumulates interest at a rate of 8\% p.a., compounded annually.

a

Plot the relationship between the number of years passed and Luke's account balance.

b

How many years will it take for the account to reach a total value of \$200?

9

Skye invests \$700 into an account which accumulates interest at a rate of 9\% p.a., compounded annually.

a

Plot the relationship between the number of years passed and Skye's account balance.

b

How many years will it take for the account to reach a total value of \$2800?

10

The value of a coin valued at \$900 appreciates in value at a rate of 8\% per year.

a

Plot the relationship between the number of years passed and the coin's value.

b

How many years will it take for the coin's value to reach a total value of \$2300?

11

The value of a plane valued at \$6500 depreciates in value at a rate of 22\% per year.

a

Plot the relationship between the number of years passed and the plane's value.

b

How many years will it take for the plane's value to reach a value of \$1100?

12

Pauline invests \$600 into a fund which accumulates interest at a rate of 8\% p.a., compounded annually.

a

Plot the relationship between the number of years passed and the value of Pauline's fund.

b

Find the value of the fund be after seven years. Round your answer to the nearest 100dollars.

13

Jimmy invests \$2000 into a fund which accumulates interest at a rate of 6\% p.a., compounded annually.

a

Plot the relationship between the number of years passed and the value of Jimmy's fund.

b

Find the value of the fund be after five years. Round your answer to the nearest 100 dollars.

14

Vincent owns a tank currently valued at \$4500 which depreciates at a rate of 28\% per year.

a

Plot the relationship between the number of years passed and the value of Vincent's tank.

b

Find the value of the tank after seven years. Round your answer to the nearest 100 dollars.

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