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)
