Question

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 $140,000 saved, and he expects to earn 10% 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 your intermediate calculations. Round your answer to the nearest cent.

Answer 1

Answer:

Computation of future value for 45,000:

Fv=PVx(1+i)ⁿ

=45,000$ x (1+0.04)¹⁰

=66,610.99

Computation of future value of his savings of140,000$ @ 10% interest rate

=Fv=PVx(1+i)ⁿ

= 140,000$ x (1+0.1)¹⁰

= 363,123.94

The father wants to withdraw 66,610.99 per year for 25 years, so present value of annuity for 25 years @10% interest rate shall be:

PV=Annual payment x PVIFA_{(10%, 25 years)} x (1+ i)

=66,610.99 x PVIFA_{(10%, 25 years)} x (1+ 10%)

= 66,610.99 x 9.0770 x 1.10

= 6,65,090.75

So now he must save around:

=(6,65,090.75-3,63,123.94)

= 3,01,966.81

Now, the 3,01,966.81 is the Fv of a 10 year annuity, the payments shall be deposited by bank at every year end 10% interest so its Annual payment = FV / FVIFA_{(rate, years)}

= 3,01,966.81 / FVIFA^{_{(10%,10 years)}}

= 3,01,966.81 / 15,937

= 18,947.53

Required annual investment is 18,947.53

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