Question

Suppose a recent college graduate's first job allows her to deposit $200 at the end of each month in a savings plan that earns 12%, compounded monthly. This savings plan continues for 13 years before new obligations make it impossible to continue. If the accrued amount remains in the plan for the next 15 years without deposits or withdrawals, how much money will be in the account 28 years after the plan began? (Round your answer to the nearest cent.)

I need to be able to see the work so I can understand how this works. I have tried so many times, and I keep getting the wrong answer. With finals coming up this will be important to know!

Thank You!

Answer 1

As per the information provided in the question

The monthly deposit by the college graduate after job (A)=$200 per month

The interest rate (r) is = 12% = 0.12 compounded monthly

Thought the interest is compounded monthly, so the Compounding period (M) in a year =12

The monthly interest rate (i) is = r/M = 0.12/12 =0.01 =1%  

Period of deposit (N) = 13years = 13x12= 156 months

Future worth (F) of the deposit after 13 years = $200(F/A,i,N) =$200(F/A,1%,156)

Future worth of the deposit (F) = $200[{(1+i)^N-1}/i]

Future worth of the deposit (F) = $200[{(1+0.01)¹⁵⁶-1}/0.01]

Future worth of the deposit (F) = $200(372.2090542530) =$74441.8109

Future worth (F) of the deposit or accrued amount after 13 years= $74441.8109

Due to new regulation the accrued amount remains in the saving plan for another 15 years, it means the accrued amount will only get interest during this 15 year

Accrued amount after 13 years= $74441.8109

Interest bearing period (N)= 15x12=180months

Future worth (F) = $74441.8109(1+i)^N

Future worth (F) = $74441.8109(1+0.01)¹⁸⁰

Future worth (F) = $74441.8109(5.9958019753)=$446,338.3568   or   Approx $446,338.36

The amount accrues in the account 28 years after the plan began is = $446,338.36