Jennifer and Rex both receive a dividend from their 401(k) retirement plan every 6 months. The earning rates for this year have been 5% per year, compounded quarterly for Jennifer, and 4.85% per year, compounded monthly for Rex. Rex felt good about this because he knew the monthly compounding on his plan would make his APY higher than Jennifer’s APY. (a) Is Rex correct? Explain your answer. (b) What is the effective rate for each plan on the basis of the payment period?

Question

What will be an ideal response?

Answer 1

(a) Find the effective annual rates

Jennifer: (1 + 0.05/4) 4 – 1 * 100% = 5.095%
Rex: (1 + 0.0485/12) 12 – 1 * 100 = 4.959%

Rex is not correct, as no frequency of compounding, even continuous, will make the
APY
go above 5%.
(b) Determine the effective i per for a 6-month payment period.
Jennifer: For a nominal rate of 2.5% semiannually, compounded quarterly, m = 2
Effective i = (1 + 0.025/2) 2 - 1 * 100 = 2.516% per 6-month period
Rex: For a nominal; rate of 2.425% semiannually, compounded monthly, m =

6

Effective i = (1 + 0.02425/6) 6 – 1 * 100 = 2.450% per 6-month period