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 6.54% 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. Enter "0" if required _______$

Answer 1

1.

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 20000*((1-(1+ 6.54/100)^-4)/(6.54/100))

PV = 68453.71

2.

Amount after withdrawal = FV year 1 - one year fees

Future value = present value*(1+ rate)^time

Future value = 68453.71*(1+0.0654)^1

Future value = 72930.58

amount = 72930.58-20000 = 52930.58

3.

amount after last withdrawal will be as deposit amount is large enough to only fund all 4 withdrawals