A couple will retire in 50 years; they plan to spend about $26,000 a year in ret

Question

A couple will retire in 50 years; they plan to spend about $26,000 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 $56,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual payment $

Explanation / Answer

We should calculat the present value of the cashflows

For the 50 years which is basically the annuity payment

PV(0.09,25,-26000,0,0)

=

Now we calcuate the investments to me made for fifty years

=PMT(0.09,50,0,-255387.07,0)

313.33

First we need to calculte the Future value of 1 at 9% for 50 years

=

FV(0.09,50,1,0,0) =815.08

X *815.08 -56000*(1.09)^30 = 255387

X =1224.88

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