Question

A couple will retire in 40 years; they plan to spend about $35,000 a year in retirement, which should last about 20 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 Savings =

b. How would the answer to part (a) change if the couple also realize that in 15 years they will need to spend $65,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Annual Savings =

Answer 1

It is assumed that the withdrawals in retirement will be at the end of each year, for 20 years.

Part (a):

Yearly withdrawal required=$35,000. Interest on savings= 9%

Amount required to be accumulated as on the date of retirement= $319,499.10

Calculated as the present value of annuity as follows:

Annual savings required during 40 years = $945.59   Calculated as follows:

Part (b):

Yearly savings required (PMT) = (PV*r)/[1-(1+r)^-n]

Where PV= Present value of future sums required, r= Rate of interest per period and n= number of times payments are to be made.

Amount to be accumulated as on date of retirement (as in part a above)= $319,499.10

Present value of the above amount= $319,499.10*PVIF(9%,40) = $319,499.10*0.03184 = $10,172.08

Amount required in 15 years for college education= $65,000

PV of the above amount= $65,000 * PVIF(9%,15) = $65,000* 0.27454 = $17,844.97

Therefore, total PV= $10,172.08 + $17,844.97 = $28,017.05

Yearly savings required= $2,604.45 Calculated as follows: