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.)

Annual Savings =

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.)

Annual Savings =

Answer 1

A. The total amount to be accumulated at the beginning of the 50 year retirement will be = 34000 x (1/1.07 + 1/1.07^2 +... 1/1.07^25) = 34000 x 1/1.07 x (1 - 1/1.07^25)/(1 - 1/1.07) = 396221.8

Hence, if the one year savings are A, the future value equation will be written as

396221.8 = A x (1 + 1.07^1 + 1.07^2 +... + 1.07^49) = A x (1.07^50 - 1)/(1.07 - 1) = 974.64

B. The future value of this 64000 will be = 64000 x 1.07^30 = 487184.32. Hence, the total value will be = 487184.32 + 396221.8 = 883406.12

883406.12 = A x (1.07^50 - 1)/(1.07 - 1)

A = 2173.046