Suppose that you are just about to retire, and you just turned 65. Your personal

Question

Suppose that you are just about to retire, and you just turned 65. Your personal and family health history is such that you forecast that you will live to age 78.

In retirement, you would like to have purchasing power of $60,000 (i.e., real dollars) before taxes. Suppose, for our example, that you anticipate receiving $20,000 in inflation-adjusted Social Security payments each year. Hence, your portfolio will need to provide $40,000 in real dollars each year. Assume that each payment is at the start of each year in retirement, where the first payment is immediately. How much do you need to have in your retirement account at retirement (in real dollars)? Assume that your portfolio earns a real annual rate of return of 4.81%, compounded annually during retirement.

Explanation / Answer

Annual Receipt of Portfolio Income = $60000

Interest Rate = 4.81%

Number of Payments = n = 14 (From Year 65 to Year 78)

As the Payment is receiving at the beginning of each year it will become annuity due and present value of annuity due will be the balance needed in retirement account

PV of Annuity Due = Annuity Amount + (Annuity Amount * (1 - (1+r)^(n-1))/r)

PV of Annuity Due = $40000 + ($40000 * (1 - (1.0481)^13)/0.0481)

PV of Annuity Due = $740016.56

Amount needed in retirement account = $740016.56

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