Question

You plan to retire in fifteen years. Since you’ll be retiring relatively young you plan to live in retirement for 25 years. You haven’t been able to save much so far and you’ve only accumulated $5,000 towards retirement. You think you will need $100,000/year to live in retirement. If you can invest at 6% annually, how much will you have to invest between now and then to achieve your goals?

Answer 1

FV of the accumulated Savings of $5,000 at the time of retirement = PV(1 + r)ⁿ

= $5,000(1.06)¹⁵

= $5,000 x 2.3966

= $11,982.79

Now, We need to find the PV of the Annual Withdrawl during retirement years;

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

= $100,000[{1 - 1.06^-25} / 0.06]

= $100,000[0.767/0.06]

= $100,000 x 12.7834 = $1,278,335.62

So, the amount each year required to be saved to get the required amount of $1,266,352.83 (=$1,278,335.62 - $11,982.79).

Annuity = [FVA x r] / [(1 + r)ⁿ - 1]

= [$1,266,352.83 x 0.06] / [1.06¹⁵ - 1]

= $75,981.17 / 1.3966 = $54,406.02