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A couple will retire in 40 years; they plan to spend about $33,000 a year in ret

ID: 2730351 • Letter: A

Question

A couple will retire in 40 years; they plan to spend about $33,000 a year in retirement, which should last about 20 years. They believe that they can earn 8% 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.) How would the answer to part (a) change if the couple also realize that in 15 years they will need to spend $63,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

a) Present value = 33000 * Cumulative Present value factor for 20 Years @ 8 %

   = 33000 * 9.81815 (approx)

= $ 323998.95

The couple will have to save $323998.95 by the retirement.

Accordingly, annual savings that the couple need to make every year = 323998.95 / [(1.08)40 - 1] / 0.08

= 323998.95 / [20.72 / 0.08]

   = 323998.95 / 259

   = $ 1250.96

Conclusion:- Couple need to save each year = $ 1250.96

b) if the couple realize that in 15 years they will need to spend $63,000 on their child’s college education:-

Present value = 63000 * Cumulative Present value factor for 15 Years @ 8 %

   = 63000 * 8.5595 (approx)

= $ 539248.50

The couple will have to save $539248.50 by the retirement.

Accordingly, annual savings that the couple need to make every year = 539248.50 / [(1.08)40 - 1] / 0.08

= 539248.50 / [20.72 / 0.08]

   = 539248.50 / 259

   = $ 2082.04

Conclusion:- Couple need to save each year = $ 2082.04

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