Question

Tim has just inherited £1000 and he decides not to invest it but rather to spend 10% of the remaining money each month. Each month Tim's saving thus reduce by a factor of 0.9 Calculate, to the nearest integer, the amount remaining (in E) after 20 months. You may find it useful to first devise a formula for the amount remaining after n months. Enter your answer, to the nearest integer and without units, in the box below. Answer:

Answer 1

£ 121.57

Explanation:

As given in question,

Total amount inherited by Tim = £1000

He spends each month = 10 % of remaining money

savings reduced each month = 0.9 of remaining amount

So, the amount of money after one month = 0.9 x £1000

amount of money remained after 2 months = 0.9 x 0.9 x £1000

amount of money remained after 3 months = 0.9 x 0.9 x 0.9 x £1000

Hence, the amount of money remained after the n months can be given by,

`E\ =\ 0.9^n* 1000`

Hence, amount of money remained after 20 months can be given by,

`E_(20)\ =\ 0.9^(20)*1000`

= £ 121.57

So, the amount of money remained after 20 months will be £ 121.57.