Question

You want to plan your retirement. Your assumption is that you will work for 25 years and after that need $200,000 annually for 20 years starting a year after you retire. In order to fund your retirement plan you want to invest the same amount at the end of each year (including the year 25) starting one year from now. How much would you have to invest each year over your working career? (Assumption with a 4% annual return to the investment).

Answer 1

First, we need to find out the amount needed at retirement

PVA = Annuity x [{1 - (1 + r)^-n} / n]

= $200,000 x [{1 - 1.04^-20} / 0.04]

= $200,000 x [0.5436 / 0.04] = $200,000 x 13.5903 = $2,718,065.27

Now, we can find the annual savings needed, by treating the above calculated PVA as FVA:

Annuity = [FVA x r] / [(1 + r)ⁿ - 1]

= [$2,718,065.27 x 0.04] / [(1.04)²⁵ - 1]

= $108,722.61 / 1.6658 = $65,266.08