I need the formula to correcty calculate this on a TI BAII Plus

You plan to retire in 18 years. At the point of retirement, you want to be able to withdraw $29798 at the end of each year forever. Assume that you earn a 8.58% rate of return prior to retirement and an 5.17% rate of return after retirement. If you do not want to make any further contributions to your retirement fund, how much do you need today? Round answer to the nearest dollar.

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Correct Answer

130978.0 margin of error +/- 2.0

This problem generates random values for your annual retirement income, years to retirement, rate of return prior to retirement and rate of return during retirement. During retirement you have a perpetuity (end of each year forever), so use the perpetuity formula to figure out how much you need at retirement (PV of a perpetuity). Once you have this value it transfers from a PV to a FV as it is now how much you want to accumulate when you retire. The amount you have now is your present value (which is what you are solving for) and there is no annuity payment (as you aren't adding to your retirement fund).