Assume that your father is now 50 years old, that he plans to retire in 10 years
ID: 2384239 • Letter: A
Question
Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $40 thousand has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year from today forward; he currently has $100 thousand saved up; and he expects to earn a return on his savings of 8 percent per year (with annual compounding). To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goals?
Explanation / Answer
First we will find out Present Value of all the future payments required on and after retirement, then we will find out payment required each year to accumulate that value in the next 10 years.
Use PV function in excel or Time Value of Money on your financial calculator;
PV of 24 annual payments is - $677,421.68 must be invested at 8% at the time of retirement to be able to get $40,000 for 24 years in real terms. So his retirement fund after adding $40,000 (required in the first year of retirement on retirement day) becomes $717,421.68
Future Value = $717,421.68
rate or I/Y = 3% after adjusting for inflation
N = 10
Present Value = $100,000 already saved up
Compute Payment = 74,304 must be saved each year to meet his retirement goals
Payment $40,000.00 Time, N 24 Future Value 0 Rate 3% (i.e. 8% minus 5% for inflation Present Value at the end of year 10 ($677,421.68)