Question

Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). You can afford to put $1,900 per quarter into the fund, and you will work for 40 years before retiring. After you retire, you will be paid a quarterly pension based on a 25-year payout. How much will you receive each quarter? (Round your answer to the nearest cent.) Please Provide a workout.

Answer 1

Given pension plan:
Quarterly payment, A = 1900
Interest per quarter, i = 0.04/12
Number of quarters, n = 40*4 = 160

Future value of pension (after 40 years)
$F=\frac{A((1+i)^n-1)}{i}$
$=\frac{1900((1+.04/12)^16--1)}{.04/12}$
$=400763.40$

As of retirement,
Present value of pension, P = 400763.40
Interest per quarter, i = 0.04/12
Number of quarters, n = 25*4 = 100
Amount of payout, A, per quarter
$A=\frac{P(i(1+i)^n)}{(1+i)^n-1}$
$=\frac{400763.40*(0.04/12*(1+0.04/12)^100)}{(1+.04/12)^100-1)}$
$=4719.23$  (to the nearest cent)