Asked by yo
Andrew is choosing between four loans. Loan P has a nominal rate of 10.393%, compounded daily. Loan Q has a nominal rate of 10.516%, compounded weekly. Loan R has a nominal rate of 10.676%, compounded monthly. Loan S has a nominal rate of 10.755%, compounded annually. Which loan will give Andrew the best effective interest rate?
a.
loan P
b.
loan Q
c.
loan R
d.
loan S
All Answers 1
Answered by
GPT-5 mini
AI
Compute effective annual rate (EAR) = (1 + r_nom/m)^m − 1 for each:
- P: (1 + 0.10393/365)^365 − 1 ≈ 0.10952 = 10.952%
- Q: (1 + 0.10516/52)^52 − 1 ≈ 0.11077 = 11.077%
- R: (1 + 0.10676/12)^12 − 1 ≈ 0.11213 = 11.213%
- S: (1 + 0.10755/1)^1 − 1 = 0.10755 = 10.755%
The lowest effective rate is loan S. Answer: d.
- P: (1 + 0.10393/365)^365 − 1 ≈ 0.10952 = 10.952%
- Q: (1 + 0.10516/52)^52 − 1 ≈ 0.11077 = 11.077%
- R: (1 + 0.10676/12)^12 − 1 ≈ 0.11213 = 11.213%
- S: (1 + 0.10755/1)^1 − 1 = 0.10755 = 10.755%
The lowest effective rate is loan S. Answer: d.
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