Question

Assume that your father is now 50 years old, plan to retired in 10 years, and expects to live for 25 years after he retires that is, until age 85. He wants his first retirement payment to have the same purchasing power at the time he retires as $40,000 has today. He wants all his consequent retirement payment to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes if inflation occurs 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 then receive 24 additional annual payments. Inflation is expected to be 5% per year from today forward. He currently has $100,000 saved and expects to earn a return on his savings of 8% per year with annual compounding. To the nearest dollar, how much must he save during each of the next 10 years to meet his retirement goal?

Answer 1

Answer:

$5,144,353.8734 This will be the amount we need to save in 10 years to achieve our goal.

Explanation:

First we will adjust the 40,000 today to the equivalent of 40,000 in ten years from now:

$Principal \: (1+ inflation)^{time} = Amount$

Principal 40,000 dollars

time 10 years

inflation   0.05000

$40000 \: (1+ 0.05)^{10} = Amount$

Amount 65,155.79 = 65,156 dollars

Then all payment will be equal to this.

So we will calcualte the present value of a 25 annuity-due of 65,156

at 8% discount rate:

$C \times \frac{1-(1+r)^{-time} }{rate}(1+r)= PV$

C 65,156

time 25

rate 0.08

$65156 \times \frac{1-(1+0.08)^{-25} }{0.08} (1+0.08) = PV$

PV $5,144,353.8734

This will be the amount we need to save in 10 years to achieve our goal.