John Adams is the CEO of a nursing home in San Jose. He is now 50 years old and

Question

John Adams is the CEO of a nursing home in San Jose. He is now 50 years old and plans to retire in 10 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, 10 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year for 10 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% per year, 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 goal? (Hint: the inflation rate 5 % per year is used only to calculate desired retirement income.)

I NEED ALL WORK SHOWN WITH FORMULAS!!

Explanation / Answer

The retirement income he retires will be given by

The nominal income he would require in 10 years would be given by = 40000*(1.05)^10 =65155.79

So we require 65115.79 each year, this becomes annuity due with =751165.35

Also he has 100,000 with him for 10 years which would give = 100000*(1.08)^10 =215892.49

Hec totalmmoney we would need is =751165.35 - 215982.49 =535272.85

Now to get 535272 in 10 year

=PMT(0.08,10,-535272,0,0)

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