A couple will retire in 40 years; they plan to spend about $21,000 a year in ret
ID: 2743683 • Letter: A
Question
A couple will retire in 40 years; they plan to spend about $21,000 a year in retirement, which should last about 20 years. They believe that they can earn 7% 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 15 years they will need to spend $51,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Annual Payment?
A couple will retire in 40 years; they plan to spend about $21,000 a year in retirement, which should last about 20 years. They believe that they can earn 7% interest on retirement savings.
Explanation / Answer
a. Present value of annuities during retirement = Annuity x PVIFA 7%, 20 years = $ 21,000 x 10.5940 = $ 222,474
This present value becomes the future value after 40 years of annuities that the couple is going to start now.
FVIFA 7%, 40 years = 199.6351
A x 199.6351 = $ 222,474
Annual payment = $ 222,474 / 199.6351 = $ 1,114.40
b. Annual payment for college education cost of $ 51,000 in 15 years, = 51,000 / 25.1290 = $ 2,029.53
Years 1-15, Annual payment = $ ( 1,114.40 + 2,029.53) = $ 3,143.93
Years 16-40 , Annual payment = $ 1,114.40
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