Question

Cheri Pie plans to make contributions to her retirement account for 40 years. After the last contribution, she will start withdrawing $2000 a month for 30 years. Assuming her account earns 6% compounded monthly, find her monthly contributions during the first 40 years needed to accomplish her goal. (Please show work, not excel).

Answer 1

calculation of monthly contribution for first 40 years:

Firstly calculate the present value of the the that will be withdraw :

monthly withdrawing amount= $2000

P.v. factor = 6%/12mnths= 0.005

period= 30 years × 12 months=390 months

P.V. = $2000× (1-(1+i)^390)/i

= $2000×171= $342000 is the vale that is to be needed to pe deposuted at the end of 40years ie future vale for year 0.

Let X be the monthly depoait in retirement account:

X = Future vale/ FVA 0.005, 480

=342000/1992 = $171.6867

he has to deposit 172 approx every month for 40 years assuming amount is to be deposited every month.