Allison and Nick anticipate they will require an annual income of $50,000 (in current dollars) when they retire 15 years from now. They expect to receive Social Security benefits of $20,000 per year at that time. In calculating their retirement savings need, the couple is assuming a 3% annual rate of inflation, an 8% return on investments, and a 25-year retirement period. Using the level payment approach, how much will Allison and Nick need to save in an annual payment at the end of each year to fund their retirement need, without considering any Social Security benefit that may be available?

Annual payment = $57,928

Explanation:

Giving the following information:

Allison and Nick anticipate they will require an annual income of $50,000 when they retire 15 years from now.

They expect to receive Social Security benefits of $20,000 per year at that time. In calculating their retirement savings need, the couple is assuming a 3% annual rate of inflation, an 8% return on investments, and a 25-year retirement period.

First, we need to calculate how much money they need on retirement:

25 years * 50000 = $1,250,000

i=8%-3% = 5%

To calculate the annual payment we need to use the following formula:

FV = {A*[ (1+i) ^n-1]}/i

A = annual payment

Isolating A:

A = (FV*i) / {[ (1+i) ^n]-1}

A = (1,250,000*0.05) / [ (1.05^15) - 1] = $57,928