Question

How much money should be deposited annually in a bank account for five years if you wish to withdraw $5,000 each year for three years, beginning five years after the last deposit? The interest rate is 3% per year

Answer 1

interest rate = 3%

Deposit at EOY1,2,3,4,5, after 5 years,i.e. at EOY 10, first withdrawal is made, the second withdrawal at EOY 11 and third withdrawal at EOY12

Let money deposited be A for five years

Future value of deposit just after last deposit, F1 = A * (F/A,3%,5)

Deposit sits for 5 more years, so value becomes F2 (EOY10) = A * (F/A,3%,5) * (F/P,3%,5)

Present value of three withdrawal of 5000 at EOY 10 = 5000 + 5000*(P/A,3%,2)

This should be equal, so

A * (F/A,3%,5) * (F/P,3%,5) = 5000 + 5000*(P/A,3%,2)

A * 5.30913 * 1.159274 = 5000 + 5000*1.913469

A * 5.30913 * 1.159274 = 14567.348

A = 2366.85