Posted by Mani on Friday, April 22, 2011 at 9:14pm.
Meg's pension plan is an annuity with a guaranteed return of 9% interest per year (compounded semiannually). She would like to retire with a pension of $70000 per semiannum for 25 years. If she works 45 years before retiring, how much money must she and her employer deposit per semiannum? (

Math  MathMate, Friday, April 22, 2011 at 9:52pm
Assume the 9% per annum interest stays fixed for the 70 years of Meg's life.
D=semiannual deposit (in first 45 years)
=70000
m=number of periods while working = 2*45=90
W=semiannual withdrawal (in last n=25 years)
n=number of periods while retired = 2*25=50
A=amount accumulated on Meg's retirement
R=semiannual interest rate = 1.045
Capital required on Meg's retirement,
First calculate A,
A=W(R^n1)/(R1)=70000*(1.045^501)/(1.0451)
=$12,495,211.98
To accumulate A over 45 years:
12495211.98=D(R^m1)/(R1)=D(1.045^901)/(1.0451)
D=12495211.98(1.0451)/(1.045^901)
=$10,910.286
Check me.
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