Question

To complete your last year in business school and then go through law school, you will need $30,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $30,000 one year from today). Your uncle offers to put you through school, and he will deposit in a bank paying 3.73% interest a sum of money that is sufficient to provide the 4 payments of $30,000 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

P.V OF ANNUITY = CASH FLOW * [ 1-(1+R)^-N] /R

=30000 [ 1-(1+0.0373)^-4] /0.03

=30000 [ 1- 0.8637] /0.03

=30000 [ 1- 0.8637] /0.03

=30000( 0.1362/0.03)

=30000*4.542

=136261.0818

APPROX 136261 IS THE AMOUNT TO BE INVESTED

TOTAL AMOUNT TO BE DEPOSTED =136261

AMOUNT OF INTEREST ARISE AT THE END OF 1ST YEAR=136261*(1+r)^N

⁼136261*(1+0.0373)¹

=136261*0.0373

=5082

AMOUNT TO BE PAID AT THE END OF FIRST YEAR=30000

AMOUNT EARNED IN THE FORM OF INTERES=5082

PRINCIPAL WITHDRAWN FROM=30000-5082=24918

AMOUNT IN BANK AT THE END OF 1ST YEAR =136261-(30000-5082)

=136261-(24918)

=111343

AMOUNT IN BANK AT THE END OF 1ST YEAR =111343

AMOUNT AFTER 4TH YEAR WILL BE ZERO

PLEASE CONSIDER IF ANY COMMENT