Question

You just turned 20 years old and want to retire when you turn 65. You plan to put $3,500 every year into a ROTH IRA, a retirement account from which you can withdraw money after retirement without having to pay any taxes. You expect to earn a return of 4% on your investments every year.  

1. How much money can you expect to have at age 65 if you make your first annual deposit now and your last one on the day you turn 64?  

2. How much money can you expect to have at age 65 if you make your first deposit 10 years from now (at age 30) and your last one on the day you turn 64?

Answer 1

Answer 1.

Annual deposit = $3,500
Interest rate = 4%
Number of deposits = 45

Accumulated sum = $3,500*1.04^45 + $3,500*1.04^44 + … + $3,500*1.04^2 + $3,500*1.04
Accumulated sum = $3,500 * 1.04 * (1.04^45 - 1) / 0.04
Accumulated sum = $3,500 * 125.870568
Accumulated sum = $440,546.99

Answer 2.

Annual deposit = $3,500
Interest rate = 4%
Number of deposits = 35

Accumulated sum = $3,500*1.04^35 + $3,500*1.04^34 + … + $3,500*1.04^2 + $3,500*1.04
Accumulated sum = $3,500 * 1.04 * (1.04^35 - 1) / 0.04
Accumulated sum = $3,500 * 76.598314
Accumulated sum = $268,094.10