MATH SOLVE

4 months ago

Q:
# 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:

Accepted Solution

A:

Answer:£ 121.57Step-by-step explanation:As given in question,Total amount inherited by Tim = £1000He spends each month = 10 % of remaining moneysavings reduced each month = 0.9 of remaining amountSo, the amount of money after one month = 0.9 x £1000 amount of money remained after 2 months = 0.9 x 0.9 x £1000amount of money remained after 3 months = 0.9 x 0.9 x 0.9 x £1000Hence, the amount of money remained after the n months can be given by, [tex]E\ =\ 0.9^n\times 1000[/tex]Hence, amount of money remained after 20 months can be given by,[tex]E_{20}\ =\ 0.9^{20}\times1000[/tex] = £ 121.57So, the amount of money remained after 20 months will be £ 121.57.