Question

To complete your last year in business school and then go through law school, you will need $35,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $35,000 one year from today). Your uncle offers to put you through school, and he will deposit in a bank paying 9.73% interest a sum of money that is sufficient to provide the 4 payments of $35,000 each. His deposit will be made today.

1. How large must the deposit be? Round your answer to the nearest cent.
   $  
   
2. 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). Calculating the Present Value today of Future periodic school payments:-

Where, C= Periodic Payments = $35,000

r = Periodic Interest rate = 9.73%

n= no of periods = 4

Present Value = $111,596.85

So, the deposit must be of $111,596.85

2) Account will earn yearly interest on deposit before 1st withdrawal is been made.

Value of account after 1st withdrawal = Deposit*(1+r)^1 - Periodic Payments

= $111,596.85*(1+0.0973)^1 - $35000

= $87,455.22

So, amount in the account immediately after you make the first withdrawal is $87,455.22

3) As the deposit is been in such a way that after earning interest on balance in account, the amount be accomadate the 4 periodic payments.

Thus, the balnace in account after 4th payment will be 0.

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