Question #165735

Assume that your father is now 50. Years old that he plans to retire in 10years and that he expects to live for 25 years after he retire.that is until he is 85 years .he wants a fixed retirement income that has the same purchasing power at the time he retires as$40000 he 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 get 24 additional annual payment.inflation is expected to be 5%per from today forward .he currently has $100000 saved up and he expects to earn a return on his saving of 8%per year annual compounding .to the nearest dollar how much must he save during each year of the next 10years with deposit being made at the end of each year to meet his retirement goal

Expert's answer

Formula: "PV = \\frac{ PMT }{ i [1 - \\frac{1 }{ (1 + i)^n}] (1 + i)}"

PMT = $40,000

i = 8%

n = Number of Years = 25

"PV = \\frac{40,000 }{ 0.08 [ 1 - \\frac{1 }{ (1 + 0.08)^{25}}](1 + 0.08)}"

PV = $461,150

So, there must be $461,150 in the account so that an annual payment of $40,000 can be withdrawn each year.

Future Value of $100,000 at 8% interest for 10 Years "= 100,000 \\times (1 + 0.08)^{10} = 215,893"

So, additional $245,257 (461,150 - 215,893) is required.

Formula to calculate annuity of future value: "FV = \\frac{PMT }{ i \\times (1 + i )^{n} - 1}"

"245,257 = \\frac{PMT }{ 0.08 (1 + 0.08)^{10}}"

PMT = $16,930

So, $16,930 is required to be deposited at the end of each year for 10 Years.

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