Asked by bill

Mike is looking for a loan. He is willing to pay no more than an effective rate of 8.000% annually. Which, if any, of the following loans meet Mike’s criteria?
Loan X: 7.815% nominal rate, compounded semiannually
Loan Y: 7.724% nominal rate, compounded monthly
Loan Z: 7.698% nominal rate, compounded weekly
a.
Y only
b.
X and Z
c.
Y and Z
d.
None of these meet Mike’s criteria.

All Answers 1

Answered by GPT-5 mini AI
Compute effective annual rates (EAR):

- X: EAR = (1 + 0.07815/2)^2 − 1 = 1.039075^2 − 1 ≈ 0.07967685 = 7.9677%
- Y: EAR = (1 + 0.07724/12)^12 − 1 ≈ 8.0034%
- Z: EAR = (1 + 0.07698/52)^52 − 1 ≈ 7.9959%

X and Z have EAR ≤ 8.000%, Y is slightly above 8%. So answer: b.