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CanadaON
Grade 9

10.02 Simple interest graphs

Worksheet
Simple interest graphs
1

The graph shows the amount of simple interest charged each year by a particular bank, on a 3-year loan:

a

Find the total amount of simple interest charged on a loan of \$5000.

b

Calculate the simple interest rate per annum, r, charged by the bank on 3-year loans.

1000
2000
3000
4000
5000
P
50
100
150
200
250
300
I
2

The given graph shows an amount of \$4000 deposited into a savings account for 10 years earning simple interest:

a

How much interest has been earned in total over the 10-year period?

b

Find the interest rate to two decimal places.

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T
3250
3500
3750
4000
4250
4500
4750
A
3

\$6000 is deposited into an account, and earns simple interest at a rate of 6\% p.a. for 10 years.

a

Complete the table of values below, calculating the interest, I, earned after n years:

n\text{ (years)}1234510
I \text{ (dollars)}\$360\$720
b

Sketch the graph of the interest earned over time.

4

Kenneth borrows \$23\,000, which generates simple interest at a rate of 3\% p.a. until he pays back the money after 5 years.

a

Complete the table of values below, calculating the interest, I, earned after n years:

n\text{ (years)}12345
I \text{ (dollars)}
b

Sketch the graph of the interest earned over time.

5

\$8000 is deposited into an account, and earns simple interest at a rate of 10\% p.a. for 5 years.

a

Complete the table of values below, calculating the interest I earned after n years:

n\text{ (years)}12345
I \text{ (dollars)}\$800
b

Sketch the graph of the interest earned over time.

c

Use the graph to determine how many years it takes to earn \$8000 in interest.

6

\$12\,000 is deposited into an account, and earns simple interest at a rate of 6\% p.a. for 6 months.

a

Complete the table of values below, calculating the interest, I, earned after n months:

n\text{ (years)}123456
I \text{ (dollars)}\$60\$120
b

Sketch the graph of the interest earned over time.

c

Use the graph of determine how many years it takes to earn \$720 in interest.

7

An amount of \$4000 is to be invested at a simple interest rate of 6\% per annum.

a

How much interest is earned each year?

b

Sketch the graph that shows the amount of the investment y, after x years.

c

Which feature of the graph represents the interest earned each year?

d

Describe the change in the graph that would occur if the amount was invested at a rate of 3 \% p.a. instead.

Compare interest rates
8

Bianca wants to take out a personal loan of \$4000, and has two options to choose from. Both Option A and Option B charge simple interest over a period of 8 years. The graphs representing the amount owing on each loan, y, after x years are shown below:

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x
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6000
7000
y
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x
1000
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7000
y
a

How much interest will she be charged each year if she goes with Option A?

b

How much interest will she be charged each year if she goes with Option B?

c

Which option will require Bianca to repay less?

d

How much less will she repay in total if she goes with Option A?

9

The following graph shows the time taken to repay a loan of \$3000 with the same sized repayments, under two different simple interest rates:

Which loan has the higher interest rate?

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x \text{ (years)}
500
1000
1500
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3000
3500
y \text{ (dollars)}
10

The following graph shows an amount of \$17\,000 being deposited into two different banks. Each bank offers simple interest at a different rate, and for different lengths of time.

a

Lisa wants her investment of \$17\,000 to grow to \$18\,000 by the time 8 years have passed. Which investment option should she take?

b

How many years longer will it take for \$17\,000 to grow to \$18\,000 under Option B than under Option A?

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x \text{ (years)}
16500
17000
17500
18000
18500
y \text{ (dollars)}
11

The graphs of two investment options are shown:

a

Which option offers the higher simple interest rate?

b

How much is initially invested under Option B?

c

After how many years do the two investments reach the same value?

d

How many more years does it take for the investment to grow to \$3500 under Option A than under Option B?

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10
x \text{ (years)}
2000
2500
3000
3500
4000
4500
y \text{ (dollars)}
12

\$1200 is to be deposited into an account that earns simple interest for 10 years. There are three available options shown in the given graph:

a

Which option earns the highest interest rate?

b

How much more is earned with Option A than earned with Option C?

c

If Option A has a \$50 setup fee, while options B and C are free to start, which is the best option for an investment of 10 years? Explain your answer.

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x \text{ (years)}
1200
1220
1240
1260
1280
1300
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1340
1360
1380
y \text{ (dollars)}
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