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 4%. He currently has $60,000 saved, and he expects to earn 7% annually on his savings. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent.

Answer 1

$45,000 now will be equal to $45,000 * (1 + 0.04)^10 = $66,610.99 after 10 years.

Hence, annuity payment after retirement for 25 years is $66,610.99

This payment is made on the retirement day. After that, he has remaining 24 payments. That is, payments are made at the beginning of the period. So present value of these annuity payments for 25 years at 7% nominal rate is given below:

• PV(60) = 66,610.99 + 66,610.99/(1+0.07)^1 + 66,610.99/(1+0.07)^2 + ...+ 66,610.99/(1+0.07)^23 + 66,610.99/(1+0.07)^24
• PV(60) = $830,594.72

Present value of this lump sum amount is discounted for 10 years to get

• PV(50) = $830,594.72 / (1+0.07) ^10 = $422,232.24

He have existing savings of $60,000.

So total amount valued currently (at age 50years) Vo =  $422,232.24 + $60,000 = $482,232.24

Vo as present value, for 10 years at 7%, annuity amount to be saved has to be found out as below:

• $482,232.24 = A / (1+0.07)^1 + A / (1+0.07)^2 + ....+ A / (1+0.07)^10
• Solving for A, we get annuity amount A = $68,659.02

So the amount he has to save for next 10 years, to have the same annuity equal to $45,000 10 years after is $68,659.02 (answer)