Question

A couple will retire in 50 years; they plan to spend about $34,000 a year in retirement, which should last about 25 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.)

b. How would the answer to part (a) change if the couple also realize that in 20 years they will need to spend $64,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

I really only need help with B. I know the answer to A is 974.65 , confirmed by the HW site. However I am really struggling with part B

Answer 1

(a): The couple will spend $34,000 from years 51-75 (25 years). At 7% interest rate the present value of these spendings at the end of 50th year = PV (7%, 25, 34000) = $396,221.83

Suppose that their annual savings is "x". Thus future value of "x" at 7% for 50 years should be $396,221.83. We can compute "x" by using this formula: PMT (7%, 50, 0, -396221.83).

This will give a value of $974.65

(b): Here value of all spendings at the end of 50th year = $396,221.83 + 64,000*1.07^30

= $883,406.15.

Thus annual savings in this case will be: PMT (7%, 50, 0, -883.406.15)

This will give an answer of $2,173.05