Question

Ten thousand dollars is deposited into a fund today. The fund earns 8% compounded annually. One year from now $20,000 will be deposited to the fund. If the funds are withdrawn in 5 equal annual amounts starting 2 years from now, how much will each withdrawal be?

Answer 1

Deposit today = $10,000

Deposit at year 1 = $20,000

Interest rate = 8%

How much will each withdrawal if the funds are withdrawn in 5 equal annual amounts starting 2 years from now?

Step 1

Calculate FV of the deposit at year 1

FV = $10,000(F/P, 8%, 1) + $20,000

FV = $10,000(1.08000) + $20,000 = 30,800

Step 2

Let the FV at year 2 is P. Convert the P into uniform A for 5 years

A = P (A/P, 8%, 5)

A = 30,800 (0.25046) = 7714

The annual withdrawals will be $7,714

Alternatively take the deposits to the end of 6^th year

FV at EOY6 = $10,000 (F/P, 8%, 6) + $20,000 (F/P, 8%, 5)

FV at EOY6 = $10,000 (1.58687) + $20,000 (1.46933) = 45,255

Convert this FV into uniform A for 5 years

A = F (A/F, 8%, 5)

A = 45,255 (0.17046) = 7,714

Five annual withdrawals will be $7,714