Question

If you deposit $5,500 at the end of each year in a Roth IRA from the age of 30 to 60 that earns 5% interest, and withdraw equal amounts of money from age 65 until 85 how much will you be able to withdraw per year?

Use compound formulas.

Answer 1

Total No. of Deposits = 60-29=31

Interest rate = 5%

Annual Deposit =$5500

Future Value of Deposits at age 60 = A*((1+r)^n-1)/r

=5500*((1+5%)^31-1)/5%

=5500*(1.05^31-1)/0.05

=5500*(4.538-1)/0.05

=5500*3.538/0.05

=$389184.34

To calculate Future value at end of year 64, n=64-60=4 years

Future Value at the end of age 64 = 389184.34*(1+5%)^4 = 389184.34*1.05^4 = 389184.34*1.2155=$473053.57

Total No of Withdrawals = 85-64 = 21

PV of withdrawal should be = $473053.57

Hence, PV = A*(1-(1+r)^-n)/r

or, 473053.57= A*(1-(1+5%)^-21)/5%

or, 473053.57= A*(1-(1.05)^-21)/0.05

or, 473053.57= A*(1-0.3589)/0.05

or, 473053.57= A*0.6411/0.05

or, A = 473053.57*0.05/0.6411

or, A = $36893.89

Hence $36893.89 can be withdrawn each year