Cambridge International Mathematics

Topics in arithmetic (Chapter 10) 221

Example 18 Self Tutor

Over a three year period the value of housing increases by6%, decreases by5%,

and then increases by8%. What is the overall effect of these changes?

Let$xbe the original value of a house.

) value after one year=$x£ 1 : 06 f6%increaseg

value after two years=$x£ 1 : 06 £ 0 : 95 f5%decreaseg

value after three years=$x£ 1 : 06 £ 0 : 95 £ 1 : 08 f8%increaseg

=$x£ 1 :087 56

¼$x£ 108 :76%

So, an 8 :76%increase has occurred.

EXERCISE 10E.2

1aIncrease$2000by20%and then by20%.

b Increase$ 3000 by10%and then decrease the result by15%.

c DecreaseE 4000 by9%and then decrease the result by11%.

d Decrease$5000by6%and then increase the result by10%.

2 True or false?

“If we increase an amount by a certain percentage and then decrease the result by the same percentage,

we get back to the original amount.”

3 Jarrod buys a wetsuit for$55to be sold in his shop. He adds40%for profit and also adds12%goods

tax. What price will he write on the sales tag?

4 Game consoles are bought by an electronics store owner for$ 120. They are marked up by55%in

order for profit to be made. After a few weeks a discount of10%is given to encourage more sales. A

goods tax of8%is applied at the point of sale. What does the customer now pay?

5 A cutlery set costs a retail shopE 65. In order to make a

profit, a45%mark up is made. As the item does not sell, two

months later the price is reduced by30%. When it is sold a

goods tax of 17 :5%is added. What is the price paid by the

customer to the nearest euro?

6 A motorcycle today costs$ 3750. The inflation rates over the next four years are predicted to be3%,

4%,5%and5%. If this occurs, what is the expected cost of the motorcycle at the end of this period?

7 If the rate of inflation is expected to remain constant at3%per year for the next 5 years, what would

you expect aE35 000car to cost in 5 years’ time?

8 An investment of$30 000is left to accumulate interest over a 4 -year period. During the first year the

interest paid was 8 :7%. In successive years the rates paid were 8 :4%, 7 :6%and 5 :9%. Find the value

of the investment after 4 years.

9 Jian invests$34 000in a fund which accumulates interest at 8 :4%per annum. If the money is left in

the fund for a 6 -year period, what will be its maturing value?

IGCSE01

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Y:\HAESE\IGCSE01\IG01_10\221IGCSE01_10.CDR Wednesday, 24 September 2008 4:49:48 PM PETER