Question

You deposit $2,500 per year at the beginning of each of the next 30 years into an account that pays 6% compounded annually. How much could you withdraw at the end of each of the 20 years following your last deposit if all withdrawals are the same dollar amount? (The 30th and last deposit is made at the beginning of the 20-year period. The first withdrawal is made at the begining of the first year in the 20-year period.)

Answer 1

Annual Savings = $ 2500 and Interest Rate = 6 % per annum, Savings Tenure =30 years beginning of period

Total Future Value of Deposits at the END of year 30 = FV30 = 2500 x (1.06)^(30) + 2500 x (1.06)^(29) +...........+ 2500 x (1.06)^(2) + 2500 x (1.06) = 2500 x [{(1.06)^(30)-1} / {1.06 - 1}] = $ 197645.4655

Let the annual withdrawals be $ K and the first withdrawal happens at the END of Year 30 and continues for the next 20 years

Therefore, 197645.4655 = K + K x (1/0.06) x [1-{1/(1.06)^(19)}]

197645.4655 = K + K x 11.15811649

197645.4655 = K x 12.15811649

K = $ 16256.2569 ~ $ 16256.26