To the nearest dollar, how much must he save over the next ten years (with deposits made at the end of each year) in order to reach his retirement goal?
The CEO of a nursing home in San Jose is John Adams. He is now 50 years old and intends to retire within the next ten years. He expects to live for another 25 years after retiring, or until he is 85. He desires a fixed retirement income with the same purchasing power as $40,000 today when he retires (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin ten years from today on the day he retires, and he will then receive 24 additional annual payments. Inflation is expected to be 5% per year for the next ten years (ignore inflation after John retires); he currently has $100,000 saved up; and he expects to earn an annual compounding return of 8% on his savings. To the nearest dollar, how much must he save over the next ten years (with deposits made at the end of each year) in order to reach his retirement goal?