Question

John Adams is the CEO of a nursing home in San Jose. He is now 50 years old and plans to retire in ten years. 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 $40,000 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, ten years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year for ten years (ignore inflation after John retires); he currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next ten years (with deposits being made at the end of each year) to meet his retirement goal? (Hint: The inflation rate 5 percent per year is used only to calculate desired retirement income.) **Please show all calculations and formulas used to derive the answers**

Answer 1

Value of $40,000 after 10 years = PV x (1 + i)^n = 40,000 x (1 + 5%)^10 = $65,155.79

Now, present value of annuity with $65,155.79 for 25 years beginning today can be calculated using PV function on a calculator with BEGIN mode

N = 25, PMT = 65,155.79, I/Y = 8%, FV = 0 => Compute PV = $695,523.42 is the amount that John needs at the end of the year 10.

He has saved $100,000 already and is willing to make 10 additional payments, which can be calculated using PMT function with END mode on a calculator

N = 10, I/Y = 8%, PV = 100,000, FV = -695,523.42 => Compute PMT = $33,108.68 is the amount John needs to deposit each year.