Your father is 50 years old and will retire in 10 years. He expects to live for

Question

Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $50,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 4%. He currently has $90,000 saved, and he expects to earn 8% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Round your answer to the nearest cent.

a. Determine the annuity payment.

b. Calculate the present value of the annuity stream.

c. Calculate the payments needed over the next 10 years to fund that annuity present value -- recognizing that he already has 90,000 saved.

Explanation / Answer

Father need to get the amount that is eqivalent to the value that of $50000 has today That means Future value of $50000 after 10 years with the available Inflation rate 4% 50000(1.04)^10= $74012.21 Needed to match purchasing power of $50,000 in 10 years. Present value of the $74012.21 additional payments in next 25 years (including the age he retires), calculated as below PV=74012.21/PVAF(8%, 25Years)= $695,523.42 This how much he will need at age 60. PV = 74012.21*10.67497         = $ 7,90,078.12 So the Father requires the amount of $790078.1 at the age of 60 years At present the father has the amount of $90000 in his hands , if he invests at the rate of 8% Below Value will reflect $90,000*(1.08^10)= $194303.20 This is the value of $90,000 in 10 years. $90000*FVF(8%,10Years) $90000*2.1589 $ 1,94,355.00 Required remaining amount = Total amount required - Amount of realisation out of depositing 90000 for 10 years @ 8% Required remaining amount = $790078.1 - $194303.20= $595774.9 $595774.9 He will have to save this much more. A=$595774.9/FVAF(8%,10years) Amount he must save each year for 10 years 1 Annuity amount = $595774.9/$14.487 $ 41,124.79 2 Present value of Annuity stream = Annuity * PVAF(8%,10Years) = 41124.79 * 6.7101 = $ 2,75,951.45 3 Refer the above claculation of arriving at $41124.79

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