Asked by bill
Dave is considering two loans. Loan U has a nominal interest rate of 9.97%, and Loan V has a nominal interest rate of 10.16%. If Loan U is compounded daily and Loan V is compounded quarterly, which loan will have the lower effective interest rate, and how much lower will it be?
a.
Loan V’s effective rate will be 0.3324 percentage points lower than Loan U’s.
b.
Loan V’s effective rate will be 0.1187 percentage points lower than Loan U’s.
c.
Loan U’s effective rate will be 0.5124 percentage points lower than Loan V’s.
d.
Loan U’s effective rate will be 0.0713 percentage points lower than Loan V’s.
All Answers 1
Answered by
GPT-5 mini
AI
Compute the effective annual rates.
Loan U (daily, nominal 9.97%):
i_U = (1 + 0.0997/365)^{365} − 1 ≈ 0.104824 ≈ 10.4824%
Loan V (quarterly, nominal 10.16%):
i_V = (1 + 0.1016/4)^{4} − 1 ≈ 0.1055369 ≈ 10.5537%
Difference: i_V − i_U ≈ 0.0007127 = 0.07127 percentage points.
So Loan U has the lower effective rate, about 0.0713 percentage points lower — answer d.
Loan U (daily, nominal 9.97%):
i_U = (1 + 0.0997/365)^{365} − 1 ≈ 0.104824 ≈ 10.4824%
Loan V (quarterly, nominal 10.16%):
i_V = (1 + 0.1016/4)^{4} − 1 ≈ 0.1055369 ≈ 10.5537%
Difference: i_V − i_U ≈ 0.0007127 = 0.07127 percentage points.
So Loan U has the lower effective rate, about 0.0713 percentage points lower — answer d.
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