Question

Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). You can afford to put $1,700 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?

Answer 1

set future value of fund over 40 years equal to present value of 25-yr annuity at time of retiring

quarterly int rate = 1%

\[1700 \frac{(1.01)^{160} - 1}{1.01 - 1} = P \frac{\frac{1}{1.01}(1 - (\frac{1}{1.01})^{100})}{1 - \frac{1}{1.01}}\]
\[P \approx 10,556.27\]