Question

You want to be able to withdraw $20,000 from your account each year for 30 years after you retire. You expect to retire in 25 years. If your account earns 10% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?

Answer 1

Amount to be withdrawn each year = P = $20000

Number of years for which withdrawals are made = n = 30

Interest rate = r = 10%

Hence, value required in account = X = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r = 20000[1- (1+0.10)^-30]/0.10 = $188538.29

Let the amount deposited each year be S

Number of deposits made = m = 25

Future Value required = $188538.28 (calculated in step above)

Hence, Future Value =  S(1+r)^m-1 +....+ S(1+r)² + S(1+r) + S = S[(1+r)^m -1]/r

=> 188538.28 = S[(1+0.10)²⁵ -1]/0.10

=> S = 188538.28*0.10/[(1+0.10)²⁵ -1] = $1917.07

Hence, he should deposit $1917.07 per year to get the required withdrawal amount