Year 10 Compound Interest Sheffield October 2016

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

Multiplication as an enlargement x2½ 40

2 ½ = 5/2 x 5/2 40

x1 ½ 18

x1½ 18 x3/2 18

x 3¼ 8

3¼ = ? x ? 26 8

x 2 4/5 20

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

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

x1½ x1½ 80 60

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?

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 £931.20 each month and he got a 5 ¾ % pay rise?

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

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

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

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.

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

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

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

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

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 £2124.46 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.

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 £540.80. 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%?