# Compound Interest (2)

In this worksheet, students answer questions based on compound interest rates given as percentages.

Key stage:  KS 4

Curriculum topic:  Ratio, Proportion and Rates of Change

Curriculum subtopic:  Set Up, Solve and Interpret Answers in Growth and Decay Problems

Difficulty level:

### QUESTION 1 of 10

Compound Interest is the amount of money earned on a sum that has been invested including the interest added each year.

It is usually written as a percentage of the money invested for each year (per annum or p.a.)

Example 1

Jack invests £250 at 1.5% compound interest p.a.

How much compound interest is earned after three years?

When we increase something by 1.5%, we can use the percentage multiplier 1.015.

After 1 year, Jack has £250 x 1.015 = £253.75

After 2 years, Jack has £253.75 x 1.015 = £257.55625

After 3 years, Jack has £257.55625 x 1.015 = £261.41959... ≈ £261.42

Compound interest earned = £261.42 - £250 = £11.42

Example 2

Jack invests £250 at 1.5% compound interest p.a.

How much compound interest is earned after ten years?

When we increase something by 1.5%, we can use the percentage multiplier 1.015.

After 1 year, Jack has £250 x 1.015 = £253.75

After 2 years, Jack has £250 x 1.015² = £257.55625

After 3 years, Jack has £250 x 1.015³ = £261.41959...

After 10 years, Jack has £250 x 1.015¹º = 290.1352...

Interest earned = £250 x 1.015¹º - £250 ≈ £40.14

Jack invests £2500 at 2% interest p.a.

How much compound interest is earned after two years?

Sue invests £200 at 2% interest p.a.

How much compound interest is earned after three years?

Bill invests £1000 at 2.5% interest p.a.

How much compound interest is earned after three years?

Fred invests £20000 at 4% interest p.a.

How much compound interest is earned after two years?

Ann invests £10000 at 6% interest p.a.

How much compound interest is earned after two years?

Amy invests £10500 at 5.5% interest p.a.

How much compound interest is earned after two years?

Amy invests £15000 at 7.5% interest p.a.

How much compound interest is earned after three years?

William invests £50000 at 3% interest p.a.

How much compound interest is earned after three years?

William invests £50000 at 3% interest p.a.

How much compound interest is earned after five years?

Kate invests £65000 at 8.5% interest p.a.

How much compound interest is earned after ten years?

• Question 1

Jack invests £2500 at 2% interest p.a.

How much compound interest is earned after two years?

101
101.00
EDDIE SAYS
2500 × 1.02²- 2500
• Question 2

Sue invests £200 at 2% interest p.a.

How much compound interest is earned after three years?

12.24
EDDIE SAYS
200 × 1.02³ - 200
• Question 3

Bill invests £1000 at 2.5% interest p.a.

How much compound interest is earned after three years?

76.89
EDDIE SAYS
1000 × 1.025³ - 1000
• Question 4

Fred invests £20000 at 4% interest p.a.

How much compound interest is earned after two years?

1632.00
1632
EDDIE SAYS
20000 × 1.04² - 20000
• Question 5

Ann invests £10000 at 6% interest p.a.

How much compound interest is earned after two years?

1236.00
1236
EDDIE SAYS
10000 × 1.06² - 10000
• Question 6

Amy invests £10500 at 5.5% interest p.a.

How much compound interest is earned after two years?

1186.76
EDDIE SAYS
10500 × 1.055² - 10500
• Question 7

Amy invests £15000 at 7.5% interest p.a.

How much compound interest is earned after three years?

3634.45
EDDIE SAYS
15000 × 1.075³ - 15000
• Question 8

William invests £50000 at 3% interest p.a.

How much compound interest is earned after three years?

4636.35
EDDIE SAYS
50000 × 1.03³ - 50000
• Question 9

William invests £50000 at 3% interest p.a.

How much compound interest is earned after five years?

7963.70
EDDIE SAYS
50000 × 1.035 - 50000
• Question 10

Kate invests £65000 at 8.5% interest p.a.

How much compound interest is earned after ten years?

81963.92
EDDIE SAYS
65000 × 1.08510 - 65000
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