A couple will retire in 50 years; they plan to spend about $20,000 a year in ret

Question

A couple will retire in 50 years; they plan to spend about $20,000 a year in retirement, which should last about 25 years. They believe that they can earn 9% interest on retirement savings.

a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual payment $.

b. How would the answer to part (a) change if the couple also realize that in 20 years they will need to spend $50,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

a.

This question needs to be solved in two steps.

First compute the total amount that the couple is required to save till the time of retirement to be able to receive $20,000 annually after retirement. This amount will be equal to the present value of an annuity of $20,000 annually for 25 years at the interest rate of 9%.

Present value of annuity of $20,000 annually for 25 years at the interest rate of 9%

= $20,000 × PVIFA (9%, 25)

= $20,000 × 9.8226

= $196,452

Therefore, till the time of retirement, the couple needs to save $196,452 to receive $20,000 per year for 25 years after retirement.

Now compute the amount that the couple needs to deposit each year to be able to save $196,452 in 50 years.

The amount that the couple needs to deposit each year can be compute by dividing $196,452 by FVIFA (9%, 50)

Amount that the couple is required to save each year

= $196,452 / FVIFA (9%, 50)

= $196,452 / 815.0836

= $241

Thus, the couple needs to save $241 per year.

b.

In this case, move this $50,000 to future and calculate the amount that the couple needs to save each year to meet both its requirement.

$50,000 is needed in year 20 which means the couple will retire 30 years after that.

Calculate the future value of $50,000 at the time of retirement.

Future value of $50,000 at the time of retirement

= $50,000 × PVIF (9%, 50)

= $50,000 × 13.2677

= $663,385

Now compute the amount that the couple needs to save each year.

Amount to be saved each year

= ($196,452 + $663,385) / 815.0836

= $1055

Thus, in this case, the couple needs to save $1055 per year.

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