Question

Currently Nathan deposits $300 at the end of each month into an IRA and his company will match 40% of his deposit amount. He will retire in 45 years. Assuming his account will earn 8.5% interest rate (APR), how much he can withdraw monthly after his retirement after-tax basis? (Assume he will live for another 25 years after retirement, his average tax rate will be 20%, and his deposit amount will remain constant).

Answer 1

Nathan deposits =					300
Employer contribution = 40% of 300=					120
So, monthly deposit in IRA total at end of the month = 300+120=					420
Time 45 years or 45*12=					540	months
Interest rate 8.5% compounded monthly
So, Monthly interest rate 8.5%/12					0.708333%
Future value of annuity (F) due at end of the period = P * { (1+r)^n - 1 } / r
420 * ((1+0.708333%)^540 - 1)/0.708333%
2621921.437
So, after 45 years, value of investments shall be $2621921.44
Afer 45 years, Annuity investment value (P)=					2621921.437
interest rate monthly (r)=					0.708333%
withdrawl amount for 25 years = 25*12=					300	months
Withdrawl amount before tax basis shall be calculated by annuity formula =
Annuity payment = P*r (1+r)^n / ((1+r)^n -1)
2621921.437 * 0.708333%*(1+0.70833%)^300/((1+0.708333%)^300-1)
21112.22578
After tax withdrawl = before tax *(1-t)
21112.22578*(1-20%)
16889.78062
So, after tax withdrawl can be made $16,889.78