Springfield mogul Montgomery Bums, age 80, wants to retire at age 100 so he can

Question

Springfield mogul Montgomery Bums, age 80, wants to retire at age 100 so he can steal candy from babies full time Once Mr. Bums retires, he wants to withdraw $0.9 billion at the beginning of each year for 10 years from a special offshore account that will pay 19 percent annually In order to fund his retirement. Mr. Bums will make 20 equal end-of-the-year deposits in this same special account that will pay 19 percent annually How much money will Mr Bums need at age 100, and how large of an annual deposit must he make to fund this retirement account If the retirement account will pay 19 percent annually, how much money will Mr. Burns need when he retires?

Explanation / Answer

We will have to calculate the present value of annual withdrawals that Mr. Burns plans to withdraw. The present value can be calculated with the use of PV function of EXCEL/Financial Calculator. The function/formula for calculating PV is PV(Rate,Nper,PMT,FV,1) where Rate = Interest Rate, Nper = Period, PMT = Annual Withdrawal, FV = Future Value (if any) and 1 indicates annuity due, since the withdrawals will be made at the beginning of each year.

__________

Using the values provided in the question, we get,

Rate = 19, Nper = 10, PMT = .9*1000,000,000 = $900,000,000 and FV = 0

Using these values in the above function/formula for PV, we get,

Amount Needed at the Time of Retirement (PV at 100 Years) = PV(19%,10,900000000*,0) = $4,646,999,242.51 or $4.647 billion (answer)

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