Question

You have $200,000 in a bank account today. It accrues interest at the rate of 6% annually. At the end of 20 years, you start withdrawing money from the account. The account still gains 6% per year on the remaining balance. How much can you withdraw per year if you want the account to last:

Answer 1

ANSWER:

If the account is to last forever then we will first find out the future value of $200,000 at 6% per year after 20 years and then the find the amount that can be withdrawn that will make the account last forever.

fv = pv(f/p,i,n)

fv = 200,000(f/p,6%,20)

fv = 200,000 * 3.207

fv = 641,400

now we will find the amount that makes the account forever.

amount = present value at 20 years(a/p,i,n)

amount = 641,400(a/p,6%,infinity)

amount = 641,400 * 0.06

amount = 38,484

so the amount that can be withdrawn per year forever after 20 years is $38,484