$1.$ $$40$K times the factor at the intersection of $5\%$ and $10$ years on the FV table $2.$ The product of $1.$ above times a factor of $11\mathrm{.}528($or $10\mathrm{.}675)$ for an Ordinary Annuity $($payment at end of period$)3.$ Current savings of $$100$K times the factor at the intersection of $8\%$ and $10$ years from the FV table $4.$ Amount needed is the difference between $2.$ and $3.$ above. $5.$ The product of $4.$ above divided by the factor at the intersection of $8\%$ and $10$ years on the FV of an Annuity table $($Annuity Due$).$ 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$$that is$,$ until he is $85.$ He wants a fixed retirement income that has the same the real value of his retirement income will decline year by year after he retires$).$ His retirement income purchasing power at the time he retires as $$40,000$ has today $($he realizes that 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 $$100,000$ saved up; and he expects to earn a return on his savings of $8$ percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next ten years $($with deposits being made at the end of each year$)$ to meet his retirement goal? $($Hint: The inflation rate $5$ percent per year is used only to calculate desired retirement income.$)65156$ Future Value of $$40,000751118\mathrm{.}368$ Total savings needed $215890$ Future Value of current savings $535228\mathrm{.}368$ Additional amount needed $$50,138\mathrm{.}49$ Required annual savings over the next $10$ years