Question

To complete your last year in business school and then go through law school, you will need $20,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $20,000 one year from today). Your uncle offers to put you through school, and he will deposit in a bank paying 3.93% interest a sum of money that is sufficient to provide the 4 payments of $20,000 each. His deposit will be made today.

How large must the deposit be? Round your answer to the nearest cent.
$

How much will be in the account immediately after you make the first withdrawal? Round your answer to the nearest cent.
$

How much will be in the account immediately after you make the last withdrawal? Round your answer to the nearest cent.
$

Answer 1

a). Calculating the initial Deposit needs to be made using the Present value of ordinary annuity formula:-

$Present Value= C*\frac{[1-(1+r)^{-n}]}{r}$

Where, C= Periodic Payments = $20,000

r = Periodic Interest rate = 3.93%

n= no of periods = 4

PresentValue = 20,000 * 20000 [1- (1 + 0.0393) - 4 0.0393

$Present Value= 20,000*\frac{[1-0.85710946468]}{0.0393}$

Present Value = $ 72,717.83

So, the large deposit amount to be is $ 72,717.83

b). Calculating the amount in the account immediately after you make the first withdrawal:-

Amount after 1st withdrawal = Initial deposit(1+r)^1 - Withdrawal amount

= $ 72,717.83(1+0.0393)^1 - $20,000

= $ 55,575.64

c). Amount after the last withdrawal will be Zero. As the initial deposit was made so that interest on outstanding balance will accumulate such that each $ 20000 payment for 4 years can be withdraw.

Hence, Balance will be nil.

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