Midterm 1 EIRQuestions

Use the following for questions 1 and 2:

Suppose you are looking at two certificates of deposit, CDs. Both are one year CDs, but
one pays, 8.00% per year compounded monthly(option A) and the other pays 8.10% compounded quarterly (option B).

1. What is the effective annual rate on the CD that pays 8% compounded monthly?

(a) 8.10%
(b) 8.00%
(c) 8.30%
(d) 8.41%

Solution:

The formula we will be using is EIR = (1 + i/p)^N – 1. The interest rate, i, is given to be 8% and is compounded monthly. The number of compounding periods in the nominal statement is p = 12 because there are 12 months in a year. The number of compounding periods (months) in desired effective period (1 year) is N = 12. Now substituting into the formula for EIR we obtain
EIR = (1 + 0.08/12)^12 – 1 = 0.0830 or 8.30%.

The answer is c.

2. Which is the better choice, option A or option B?

(a) A
(b) B

Solution:

Since we are deciding between CD’s we want the one with the higher EIR. We already know the EIR for option A so now we need to find the EIR for option B. Option B is also a one year CD but it pays 8.10% and is compounded quarterly, so p = 4 = N. Now we substitute and get EIR = (1 + 0.081/4)^4 -1 = 0.0835 or 8.35%. Since the EIR for option B is greater than the EIR for option A, we choose option B.

The answer is b.

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