Question

Upon graduating from college 30 years​ ago, Dr. Nick Riviera was already thinking of retirement. Since then he has made deposits into his retirement fund on a weekly basis in the amount of ​$30. Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned 7.8​% interest compounded weekly.

a. How much has Nick accumulated in his retirement​ account?

b. In addition to all​ this, 10 years​ ago, Nick received an inheritance check for ​$30,000 from his beloved uncle. He decided to deposit the entire amount into his retirement fund. What is his current balance in the​ fund?

Answer 1

(a)

Given

Weekly Deposit Amount (A) = 30$

Number of years he deposited them (n)= 30 Years

Frequency of deposits (m) = 52 times in an year

Interest (r) = 7.8%

Question is how much is accumulated in his account that is future value of weekly deposit (FVA)=?

Formula for Calculating it is as follows

FVA = A*{(((1+(r/m))*(m*n)) - 1) / (r/m)}

= 30*{(((1+(0.078/52))*(52*30)) - 1 / (0.078/52)}

= 30*6242.0344

=187,261.0327$

The amount that he accumulates at his retirement = 187,261.0327$

(b)

Given 30,000$ have been deposited 10 years ago and he has deposited same amount in retirement fund. In order to know total amount accumulated in retirement fund, we have to compute future value of the amount deposited and add it to the amount that we have computed above in solution (a)

Future Value = Present Value / (1+Rate)^Number of years (Since it is one time investment)

= 10000*(1+0.078)^10

= 21,192.7643$

Total Amount that is accumulated in his retirement fund would be 187,261.0327 + 21,192.7643 = 208,453.7970$