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.
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) [tex]F=\frac{A((1+i)^n-1)}{i}[/tex] [tex]=\frac{1900((1+.04/12)^16--1)}{.04/12}[/tex] [tex]=400763.40[/tex]
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 [tex]A=\frac{P(i(1+i)^n)}{(1+i)^n-1}[/tex] [tex]=\frac{400763.40*(0.04/12*(1+0.04/12)^100)}{(1+.04/12)^100-1)}[/tex] [tex]=4719.23[/tex] (to the nearest cent)
