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 $45,000 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 5%. He currently has $180,000 saved, and he expects to earn 7% 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.

Answer 1

Amount needed to match the purchasing power of $45,000 in 10 years:

= P(1 + r)^n = $45,000(1.05)^10 = $45,000 x 1.6289 = $73,300.26

Amount needed at age 60:

PVA = P[{1 - (1 + r)^-n} / r]

= $73,300.26[{1 - 1.07^-25} / 0.07]

= $73,300.26[0.8158 / 0.07]

= $73,300.26 x 11.6536 = $854,210.66

Value of $180,000 in 10 years:

FV = PV(1 + r)ⁿ

= $180,000(1.07)¹⁰ = $180,000 x 1.9672 = $354,087.24

He will have to save:

= $854,210.66 - $354,087.24 = $500,123.41

Amount to be saved each year for 10 years:

A = [PVA x r] / [1 - (1 + r)^-n]

= [$500,123.41 x 0.07] / [1 - 1.07^-10]

= $35,008.64 / 0.4917 = $71,206.32