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 $40,000 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 6%. He currently has $95,000 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? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Current value of Annual Retirement Amount = $40000

Time to retirement=10 years

Hence, Annual Retirement Value required at the time of retirement = 40000*(1+6%)^10 = 40000*1.06^10 = 40000*1.7908 = $71633.91

PV of retirement payments at the time of retirement = 71633.91+PV of 24 annual payments

PV of 24 payments = A*(1-(1+r)^-n)/r

=71633.91*(1-(1+8%)^-24)/8%

=71633.91*(1-1.08^-24)/0.08

=71633.91*(1-0.1577)/0.08

=71633.91*0.8423/0.08

=754216.12

PV of retirement payments at the time of retirement = 71633.91+754216.12=$825850.03

Current Saving=$95000

FV of current investment at the time of retirement=95000*(1+8%)^10=95000*1.08^10=95000*2.1589=$205097.87

Hence Net FV Required at the time of retirement = 825850.03-205097.87=$620752.16

Hence annual Saving required to achieve $620752.16 will be given by FV=A*((1+r)^n-1)/r

or, 620752.16 = A*((1+8%)^10-1)/8%

or, 620752.16=A*(1.08^10-1)/0.08

or, 620752.16 =A*(2.1589-1)/0.08

or, 620752.16=A*1.1589/0.08

or, A =620752.16*0.08/1.1589

or, A = $42850.20

Hence Annual Saving Required is $42850.20