Question

You have just turned 40 years old and are trying to decide who much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 7% per year. You cannot make withdrawals until you retire on your sixty-fifth birthday. After that point, you can make withdrawals as you see fit. You decide that you will plan to live to 95 and work until your turn 65. You estimate that to live comfortably in retirement, you will need $250,000 per year starting at the end of the first year of retirement and ending on your 95th birthday. You already have $200,000 in the retirement plan. You will contribute the same amount to the plan at the end of every year that you work, starting next year. How much do you need to contribute each year to fund your retirement

Answer 1

$31,886.09

Step-by-step explanation:

years until retirement = 65 - 40 = 25 years

interest earned 7%

retirement age 65

expected life span after retiring = 95 - 65 = 30 years

financial needs during retirement $250,000 per year

current account balance $200,000

we must first determine how much money you will need when you are 65:

present value = $250,000 x 12.409 (PV annuity, 30 years, 7%) = $3,102,250

your $200,000 will be worth $200,000 x (1 + 7%)²⁵ = $1,085,486.53 in 25 years

so you need $3,102,250 - $1,085,486.53 = $2,016,763.47 extra

using the FV formula for an annuity:

$2,016,763.47 = payment x 63.249 (FV annuity, 25 years, 7%)

payment = $2,016,763.47 / 63.249 = $31,886.09