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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 £) 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.

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 £) 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.

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Solution

The formula for the amount remaining after n months, given that Tim spends 10% of the remaining money each month, is:

A = P * (0.9^n)

where: A is the amount remaining, P is the principal amount (the initial amount of money), n is the number of months, and 0.9 is the remaining percentage of money after spending 10% each month.

Substituting the given values into the formula:

A = 1000 * (0.9^20)

Calculating the above expression gives:

A ≈ 121.58

Rounding to the nearest integer, the amount remaining after 20 months is approximately £122.

This problem has been solved

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