Question

A man has deposited $50,000 in a retirement income plan with a local bank. This bank pays 8% per year, compounded annually, on such deposits. What is the maximum amount the man can withdraw at the end of each year and still have the funds last for 12 years? Suppose that a person deposits $500 in a savings account at the end of each years, starting now for the next 12 years. If the bank pays 8% per year, compounded annually, how much money will accumulate by the end of the 12 year period?

Answer 1

Part 1) We have the following information

Initial deposit = $50,000

Let the annual withdrawal be X

Life (n) = 12 years

Interest rate (i) = 8% or 0.08 per year

Using net present worth (NPW) technique

NPW = Initial deposit – Annual withdrawal(P/A, i, n)

0 = 50000 – X(P/A, 8%, 12)

0 = 50000 – X[((1+0.08)¹² – 1)/0.08 (1+0.08)¹²]

0 = 50000 – 7.536X

7.536X = 50000

X = $6,634.75

Part 2) We have the following information

Annual deposit = $500

Life (n) = 12 years

Interest rate (i) = 8% or 0.08 per year

Future worth = 500(F/A, 8%, 12)

Future worth = 500[((1 + 0.08)¹² – 1)/0.08]

Future worth = 500 × 18.977

Future worth = $9488.56

So, the amount accumulated by the end of the 12 year period = $9,488.56