Topics
5. Interest, investments and loans
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AustraliaNSW
Year 12

5.02 Comparing simple and compound interest

Lesson
Worksheet
Practice
Worksheet
Compare simple and compound interest
1

Describe the difference between compound and simple interest.

2

If \$1000 is invested for 4 years with an interest rate of 5\% per annum, calculate the final balance if:

a

Simple interest was used.

b

Compound interest was used, compounding annually.

3

If \$100\,000 is invested for 4 years with an interest rate of 10\% per annum, calculate the final balance if:

a

Simple interest was used.

b

Compound interest was used, compounding annually.

4

The following table shows the bank balance of two accounts. Sean invested in a simple interest yielding account for 3 years at 7\%, and Caitlin invested in a compound interest account, compounding annually for 3 years also at 7\%:

PrincipalYear 1Year 2Year 3
Account A\$1000\$1070.00\$1144.90\$1225.04
Account B\$1000\$1070.00\$1140.00\$1210.00

According to the data, which account is Sean's?

5

The following table shows the value of an investment when invested under different conditions:

PrincipalYear 1Year 2Year 3Year 4Year 5Year 6
Investment 1\$500\$535.00\$572.45\$612.52\$655.40\$701.28\$750.37
Investment 2\$500\$537.51\$575.01\$612.52\$650.03\$687.54\$725.04
a

After 6 years which investment is worth more?

b

If an investor only has 2 years to invest, which investment should they choose?

c

At what year are the investments worth the same amount?

Compare interest graphs
6

\$100 is invested for 10 years with an interest rate of 10\% p.a. that includes the accumulated interest.

a

Is this an example of simple or compound interest?

b

State whether the following graphs represent the growth of the investment:

i
2
4
6
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10
T\text{(years)}
50
100
150
200
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300
\text{Investment}(\$)
ii
2
4
6
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10
T\text{(years)}
50
100
150
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250
300
\text{Investment}(\$)
7
a

Consider the graph shown on the right:

i

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

ii

How much is invested in the account?

iii

How much is the investment worth after 10 years?

5
10
15
\text{Years}
1
2
3
4
5
\text{Investment}(\$1000\text{s})
b

Consider the following three graphs:

Graph A

2
4
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18
\text{Years}
1
2
3
4
5
\text{Investment}(\$1000\text{s})

Graph C

2
4
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\text{Years}
1
2
3
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5
\text{Investment}(\$1000\text{s})

Graph B

2
4
6
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10
12
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16
18
\text{Years}
1
2
3
4
5
\text{Investment}(\$1000\text{s})
i

Are the investments accruing simple or compound interest? Explain your answer.

ii

How much is invested in each option?

iii

How much is each investment worth after 10 years?

iv

Which is the best investment?

v

Which of the graphs yield the same investment as the graph in part (a) after 10 years?

8

Which of the following graphs represent a savings account that earns:

a

Compound interest over 50 years.

b

Simple interest over 5 years.

A
\text{Years}
\text{Balance}
B
\text{Years}
\text{Balance}
C
\text{Years}
\text{Balance}
D
\text{Years}
\text{Balance}
9

The following graph shows both an investment with simple interest, and one with compound interest, labelled Investment A and Investment B respectively.

a

Which investment has a higher principal amount?

b

Which investment has a higher final amount after 10 years?

c

After how many years are the investments equal in value?

5
10
15
\text{Years}
2
4
6
8
\text{Investment } (\$1000\text{s})
10

Lucy has a choice of two savings accounts:

  • Deposit of \$7000 earns 5\% simple interest per annum.
  • Deposit of \$6500 earns 5\% compound interest per annum.

The future value of these accounts over the first 25 years are shown in the graph below:

a

State the equation that describes the future value, FV of the simple interest account after n years.

b

State the equation that describes the future value, FV of the compound interest account after n years.

c

Using the graphs provided, which account would have a greater balance after:

i

5 years?

ii

18 years?

d

After how many whole years will the value of the account with compound interest be higher than the account with simple interest?"

2
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n \text{ (years)}
2
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FV (\$1000\text{s})
11

Teo has a choice of two savings accounts:

  • Deposit of \$3600 earns 2.9\% simple interest per annum.
  • Deposit of \$3450 earns 2.8\% compound interest per annum.

The future value of these accounts over the first 30 years are shown in the graph below:

a

State the equation that describes the future value, FV of the simple interest account after n years.

b

State the equation that describes the future value, FV of the compound interest account after n years.

c

Using the graphs provided, which account would have a greater balance after:

i

6 years?

ii

29 years?

d

What is the value of the investments when they reach equal value?

10
20
n \text{ (years)}
1
2
3
4
5
6
7
8
9
FV (\$1000\text{s})
12

A bank offers two types of savings accounts:

  • Deposits of \$2400 accrue 2.9\% simple interest per annum.
  • Deposits of \$1350 accrue 2.8\% compound interest per annum.

The future value of these accounts over the first 20 years are shown in the graph below:

a

State the equation that describes the future value, FV of the simple interest account after n years.

b

State the equation that describes the future value, FV of the compound interest account after n years.

c

Using the graphs provided, which account would have a greater balance after 11 years?

d

Will the account earning compound interest ever have a larger balance than the account earning simple interest?

2
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n \text{ (years)}
1
2
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8
9
FV (\$1000\text{s})
13

Consider the following investment options:

  • Option A: \$3300 invested at 2.9\% p.a. simple interest.
  • Option B: \$3150 invested at 2.8\% p.a. compound interest.
a

State the equation that describes the future, FV of the simple interest option after n years.

b

State the equation that describes the future value, FV of the compound interest option after n years.

c

Sketch the graph of the equation in part (a).

d

Sketch the graph of the equation in part (b).

e

Which option will have a greater balance in 25 years?

14

A bank offers two types of savings accounts:

  • Deposits of \$5000 earn 5\% simple interest per annum.
  • Deposits of \$4500 earn 5\% compound interest per annum.
a

State the equation that describes the future value, FV of the simple interest account after n years.

b

State the equation that describes the future value, FV of the compound interest account after n years.

c

Sketch the graph of the equation in part (a).

d

Sketch the graph of the equation in part (b).

e

Which account will have a greater balance after 2 years?

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Outcomes

MS2-12-5

makes informed decisions about financial situations, including annuities and loan repayments

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