Help! I'm really stuck on this problem - Here is the problem in text book - 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 retiresthat 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.)

Here are the calculations I've done so far:

Where I'm stuck is how I calculate how much he needs to save per year .

In order to figure out how much money $40,000 equals in 10 years, I took the present value of $40,000 and assumed the 5% interest rate fit in here.

FV= PV*(1+i)n

FV=$40,000*

FV= $40,000*

FV= $40,000*1.63

FV= $65,200 per year for retirement

There for, if Joe withdrawals 24 annuities of $65, 200 for 24 years, he will need a present value of $686,475.04.

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If Joe does no additional savings, this is how much he will have.

FV= PV (1+i)n

FV= $100,000*(1+.08)10

FV= $100,000*(1.08)10

FV= $100,000*2.15

FV= $215,892.50

Therefore Joe needs to save $686,475.40 (PV) -215,892.50 (FV) for the future $470,681 /10

(OR$686,457 PV-100,000 PV of savings)= $586,475 (but grows at 8% annual compound)