1. Year 10 Compound Interest
Sheffield
October 2016

2. Have a go at these on your mini-whiteboard
2 ½ lots of 40 1 ½ lots of 18 3 ¼ lots of 8 2 3/5 lots of 20
Extension
Explain why a half of something isn’t necessarily bigger than a quarter of something else

3. Multiplication as an enlargement
x2½ 40

4. 2 ½ = 5/2
x 5/2 40

5. x1 ½ 18

6. x1½ 18
x3/2 18

7. x 3¼ 8

8. 3¼ = ?
x ? 26 8

9. x 2 4/5 20

10. Extension Explain why a half of something isn’t necessarily bigger than a quarter of something else

11. Consider the two questions …
Increase 80 by 50% Increase 60 by 50%

12. x1½
x1½ 80 60

13. Is there a general rule we can use?
What’s the connection?
If increase by 50% is essentially same as x 1 ½ or x 1.5
Increase by 25% = or
Increase by 10% = or
= x 1 1/5 or
= or x 1.05
Is there a general rule we can use?

14. Which is the better method?
Bill earns £800 per month. He gets a pay rise of 6% Can you write down two different ways of calculating his new wage?
Which is the better method?
Would it make a difference if his wage was £ each month and he got a 5 ¾ % pay rise?

15. Imagine you bought something on a credit card for £120 which charges 4% interest per calendar month.

16. What does the diagram represent?
x1.04
x1.04
x1.04
120

17. What does the calculation represent?
120 x (1.04)3

18. Investing money
Match up the cards illustrating an investment through words, diagrams & calculations. For every example there should be three cards but some examples have a card missing. Write what should be on the missing cards and calculate the final amount each investment becomes.

19. An investment of £240 is made for three years at an interest rate of 5% per year
£240 x (1.05)3
x1.05
x1.05
x1.05
240

20. An investment of £160 is made for three years at an interest rate of 6½ % per year
£160 x (1.065)3

21. An investment of £500 is made for two years at an interest rate of 4¾ % per year .
x1.0475
X1.0475
500

22. £200 x (1.04)2 x (1.06)2
x1.04
x1.04
x1.06
x1.06
200

23. Katy invests £2000 in a savings account for 3 years
Katy invests £2000 in a savings account for 3 years. The account pays compound interest at an annual rate of 2.5% for the first year x% for the second year x% for the third year There is a total amount of £ in the savings account at the end of 3 years. Work out the rate of interest in the second year. Show clearly how you found your answer.

24. Problems to consider
£500 is invested for 2 years at a set interest rate payable each year. After the 2 year term the investment is now worth £ What was the annual rate of interest? A sum of money is invested and after 3 years it is now worth 33.1% more than the original investment. What was the annual rate of interest? A credit card charges monthly interest. Its annual rate on interest works out to be approximately 24% What is the monthly interest rate to the nearest 0.1%?