How interesting! On my daughter’s date of birth, I start depositing $250 at the

Question

How interesting! On my daughter’s date of birth, I start depositing $250 at the end of every month into a bank account. The account earns 4.8% interest compounded monthly. (a) How much will be available in the account on my daughter’s 18th birthday? (b) At that time, she will start making withdrawals at the beginning of each month for the next 5 years, eventually depleting the account. What is the size of each withdrawal? (c) Comparing her withdrawals and my deposits, how much interest was earned on my investment?

Explanation / Answer

Interest rate = 4.8% per annum = 0.4% per month compunded monthly

a) We are depositing 250$ each month for 18 years. We can calculate the maturity value after 18 years using the foloowing formula in excel:

Maturity value = FV(interest rate per period, no.of installments,monthly installment value, present value, end of period) = FV(0.004,216,250,0,0) = 85534 $

So at the end of 18th birthday the account will contain 85,534 $.

b) Now after 18th birthday, the daughter will start withdrawing some amount (let us assume x) at the beginning of each month. Assume that the father is still depositing 250$ per month in the account. We have to find out the value for x, such that at the end of five year the money in the account becomes zero. We can calclate this value using PMT function in excel:

x= 250$ + PMT (ineterst rate per month, number of periods, present value, future value, beginning of month)

x = 250 + PMT(0.004,60,85534,0,1) = 250 + 1599.9 = 1850 $ per month.

So the daughter can withdraw 1850$ per month over a period of 5 years starting from her 18th birthday.

c) Interest earned over the whole investment = (Total amount withdrawn by the daughter in 5 years) - (Total amount deposited by the father in 23 years) = (5*12*1850) - (23*12*250) = 1,11,000 - 69,000 = 42,000 $

So the final answer is Interest earned over the whole investment = 42,000 $

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