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Required Lump-Sum Payment To complete your last year in business school and then go through law...

Required Lump-Sum Payment

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 8.4% interest a sum of money that is sufficient to provide the 4 payments of $20,000 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

Solutions

Expert Solution

How large must the deposit be?

The value of deposit will be equal to the sum of present value of all future payments

Present value can be calculated by discounting the future payments at 8.4% interest rate

Therefore,

The value of deposit = $20,000/ (1+ 8.4%) ^1 +$20,000/ (1+ 8.4%) ^2 +$20,000/ (1+ 8.4%) ^3 +$20,000/ (1+ 8.4%) ^4

=$18,450.18 +$17,020.47 +$15,701.54 +$14,484.81

= $65,657.00

How much will be in the account immediately after you make the first withdrawal?

First withdrawal is after one year, that time initial deposit will grow equal to

= $65,657.00 * (1+ 8.4%)

=$71,172.19

First withdrawal amount is $20,000

Therefore,

The amount in the account immediately after you make the first withdrawal = $71,172.19 - $20,000

=$51,172.19

How much will be in the account immediately after you make the last withdrawal?

The amount in the account immediately after you make the last withdrawal will be zero.

jeff jeffy answered 11 months ago
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