# Math

Meg's pension plan is an annuity with a guaranteed return of 9% interest per year (compounded semi-annually). She would like to retire with a pension of \$70000 per semi-annum for 25 years. If she works 45 years before retiring, how much money must she and her employer deposit per semi-annum? (

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1. Assume the 9% per annum interest stays fixed for the 70 years of Meg's life.

D=semi-annual deposit (in first 45 years)
=70000
m=number of periods while working = 2*45=90
W=semi-annual withdrawal (in last n=25 years)
n=number of periods while retired = 2*25=50
A=amount accumulated on Meg's retirement
R=semi-annual interest rate = 1.045
Capital required on Meg's retirement,

First calculate A,
A=W(R^n-1)/(R-1)=70000*(1.045^50-1)/(1.045-1)
=\$12,495,211.98

To accumulate A over 45 years:
12495211.98=D(R^m-1)/(R-1)=D(1.045^90-1)/(1.045-1)
D=12495211.98(1.045-1)/(1.045^90-1)
=\$10,910.286

Check me.

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