Asked by julie
Melanie is looking for a loan. She is willing to pay no more than an effective rate of 9.955% annually. Which, if any, of the following loans meet Melanie’s criteria?
Loan A: 9.265% nominal rate, compounded weekly
Loan B: 9.442% nominal rate, compounded monthly
Loan C: 9.719% nominal rate, compounded quarterly
a.
B only
b.
A and C
c.
A and B
d.
None of these fit Melanie’s criteria.
All Answers 1
Answered by
GPT-5 mini
AI
Use the effective annual rate formula: EAR = (1 + r_nom/m)^m − 1.
Loan A: r = 0.09265, m = 52
EAR_A = (1 + 0.09265/52)^52 − 1 ≈ 0.09693 ≈ 9.693%
Loan B: r = 0.09442, m = 12
EAR_B = (1 + 0.09442/12)^12 − 1 ≈ 0.09862 ≈ 9.862%
Loan C: r = 0.09719, m = 4
EAR_C = (1 + 0.09719/4)^4 − 1 ≈ 0.10079 ≈ 10.079%
Melanie’s cap is 9.955%, so A and B meet her criterion, C does not. Answer: c.
Loan A: r = 0.09265, m = 52
EAR_A = (1 + 0.09265/52)^52 − 1 ≈ 0.09693 ≈ 9.693%
Loan B: r = 0.09442, m = 12
EAR_B = (1 + 0.09442/12)^12 − 1 ≈ 0.09862 ≈ 9.862%
Loan C: r = 0.09719, m = 4
EAR_C = (1 + 0.09719/4)^4 − 1 ≈ 0.10079 ≈ 10.079%
Melanie’s cap is 9.955%, so A and B meet her criterion, C does not. Answer: c.
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