# math

posted by patrick

Meg's pension plan is an annuity with a guaranteed return of 3% per year (compounded quarterly). She would like to retire with a pension of \$50,000 per quarter for 5 years. If she works 21 years before retiring, how much money must she and her employer deposit each quarter?

1. Reiny

Let's pick the date of her retirement as a reference point (focal point).
i = .03/4 = .0075
n for working period = 21(4) = 84
n for retirement period = 5(4) = 20
let her and her employer's contribution be x

So the "amount" of the contributions = Present Value of her annuities at that time.
x(1.0075^84 - 1)/.0075 = 50,000(1 - 1.0075^-20)/.0075
multiply both sides by .0075
x(1.0075^84 - 1) = 50,000(1 - 1.0075^-20)
x(.87320...) = 50000(.1388101...)
x = 7948.34

check my arithmetic

strange pension. So she is allowing her retirement to last only 5 years, with an annual income of appr. \$200,000 ?
Looks like she is going to live it up for 5 years, and then .... ???

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