Question

Anne-Marie and Yancy calculate their current living expenditures to be ?$64,000 a year. During retirement they plan to take one cruise a year that will cost ?$5,000 in? today's dollars.? Anne-Marie estimated that their average tax rate in retirement would be 11 percent. Yancy estimated their Social Security income to be about ?$18,236 and their retirement benefits are approximately ?$28,044. Use this information to answer the following? questions: a. How much? income, in? today's dollars, will? Anne-Marie and Yancy need in retirement assuming 70 percent replacement and an additional ?$5,000 for the? cruise? b. Calculate their projected annual income shortfall in? today's dollars. c.? Determine, in? dollars, the future value of the shortfall 29 years from? now, assuming an inflation rate of 3 percent. d. Assuming a nominal rate of return of 8 percent and 22 years in? retirement, calculate their necessary annual investment to reach their retirement goals.

Answer 1

Part a:

Yearly income requirement = (Current living expenses $64,000 * Replacement rate 70% + Cruise cost $5,000) / (1-tax rate 11%)

Yearly income requirement = $55,955.05

Part b:

Projected yearly income shortfall = (Retirement benefits $28,044 + Social security $18,236) - (Current living expenses $64,000 * Replacement rate 70% + Cruise cost $5,000)

Projected yearly income shortfall = $9,675.056

Part c:

Future value of yearly income shortfall = Projected yearly income shortfall $9,675.056 * (1+ Inflation rate 3%)^{Number of years 29}

Future value of yearly income shortfall = $22,799.90

Part d:

Since nothing is mentioned about the current age of Anne-Marie and Yancy and their life expectance, hence assuming their current age is 48, they'll retire after 22 years at 60 years of age and they'll survive till age of 80 years.

Step1: At the age of retirment i.e. after 22 years, calculate the present value of income shortfall till death (20 years)

Step 2: Find the future value of current equal annual savings which should equate to the present value of income shortfall in 22 years from now.

Future value $227,096.27 = Annual Savings * {(1+Nominal Rate 8%)^{Number of years 22} - 1}/Nominal rate 8%

Annual savings = Future value $227,096.27 / {(1+Nominal Rate 8%)^{Number of years 22} - 1}/Nominal rate 8%

Annual savings = $4,095.02 to reach to their requirement goals