Question

You plan to retire in year 20 Your retirement will last 25 years. You want to have $65,000 each year of your retirement. How much would you have to invest each year, starting in one year, for 15 years , to exactly pay for your retirement ,if your investments earn 6.00% APR (compounded annually)?

Answer 1

Annual payment after retirement = $65,000
Interest rate = 6%
Number of payments = 25

Amount required at retirement = $65,000 * PVIFA(6%, 25)
Amount required at retirement = $65,000 * (1 - (1/1.06)^25) / 0.06
Amount required at retirement = $65,000 * 12.783356
Amount required at retirement = $830,918.14

Time to retirement = 5 years
Number of deposits = 15

Annual deposit * FVIFA(6%, 15) * FVIF(6%, 5) = $830,918.14
Annual deposit * (1.06^20 - 1) / 0.06 * 1.06^5 = $830.918.14
Annual deposit * 49.227419 = $830,918.14
Annual deposit = $16,879.17

So, you need to deposit $16,879.17 each year