Amy Plisko is 23 years old and plans to retire in 32 years when she is 55 years

Question

Amy Plisko is 23 years old and plans to retire in 32 years when she is 55 years old. Amy just graduated from a university in the West. Upon graduation, she took a job with a starting annual salary of $50,000. Amy asks you to answer the following two questions: 1. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of inflation over the past 80 years (about 3% per year), how large will her annual salary be in her last year before retirement? (Use 32 years.) 2. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of return on common stocks over the past 80 years (about 10.5% per year), how large will her annual salary be in her last year before retirement? (Use 32 years.) After hearing your answers, Amy says, "WOW! That's quite a difference." She decides that she would like an income of $500,000 per year each year in retirement, provided in equal annual end-of-the-year cash flows. These cash flows need to last for 40 years, and her investments would earn an annual rate of return of 7% during her retirement. Amy's final question to you is how much money must she save in equal annual end-of-the-year cash flows for the next 32 years to provide for her desired retirement, if her investments earn roughly the same rate of return as those earned by U.S. small stocks over the last 80 years (geometric average is about 12% per year)

Explanation / Answer

1. Current Salary = $50,000

Rate of interest = 3%

Salary (after 32 years) = PV * (1+r)^32

i.e. Salary (after 32 years) = 50,000 * 1.03^32 = $128,754.14

2.Now interest rate is 10.5%

Salary after 32 years = 50,000*1.105^32 = $1,220,570.6

Now we need to Calcualte the PV at the start of her retirement so that she will be able to withdraw $500,000 for 40 years. Investmenr earns a rate of 7% return.TO calculate the PV, enter the following in the financial calculator

PMT = 500,000; 1/y = 7%, n=40, FV = 0, calcualte PV = $6,665,854.4

Thus we need $6,665,854.4 in account at the start of the retirement in order to have $500,000 for 40 years.

Now in order to get this corpus, lets calculate the annual savings. Enter the following int he financial calculator.

FV = 6665,854; 1/y = 12%, n=32, Pv = 0, calcualte PMT = $21,866

SO, she needs to save $21,866 for her desired cash flows in the retirement period.

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