Question

John Decides to make 10 end-of year deposits of $10,000 into a fund starting one year from now. He is planning to withdraw $20,000 each year for 5 years, starting one year after the last deposit. The fund pays 8% per year compounded annually. Determine the balance in the fund immediately after the last withdrawal.

Answer 1

As per the question Jhon deposits $10000 in a fund for 10 year

Annual deposits (A) = $10000

Period of deposit (N) = 10 years

Rate of interest (i) = 8% per year

The future value of saving at 10^th year= 10000(F/A,8%,10) = 10000(14.4866) = $144866

(The future value of saving without annual deposit from 11^th year to 15^th year)

The future value of saving at 15^th year = 144866(F/P,8%,5) = 144866(1.4693)= $212851.61

As per the question john plans to withdraw $20000 each year for 5 year, after one year of last deposit. (Accordingly John withdraw from 11^th year to 15^th year)

Annual withdraw (A) = $20000

Period of withdraw (N) = 5 years

Rate of interest (i) = 8% per year

Future value of the withdraw at 15^th year = 20000(F/A,8%,5) = 20000(5.8666) = $117332

The balance in the fund at 15^th year = Future value of saving at 15^th year - Future value of the withdraw at 15^th year

The balance in the fund at 15^th year = 212851.61 – 117332 = $ 95519.61 or Approx $95520

The balance in the fund immediately after last withdraw is $95520