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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