Asked by eman
RJ has two loans. Loan H has a nominal rate of 5.68%, compounded daily. Loan I has a nominal rate of 6.33%, compounded monthly. Which loan's effective rate had the greater increase, relative to its nominal rate, and how much greater is its increase than that of the other loan?
a.
Loan I’s increase was 0.03 percentage points greater than Loan H’s.
b.
Loan I’s increase was 0.68 percentage points greater than Loan H’s.
c.
Loan H’s increase was 0.16 percentage points greater than Loan I’s.
d.
Loan H’s increase was 0.49 percentage points greater than Loan I’s.
Please select the best answer from the choices provided
A
B
C
D
All Answers 1
Answered by
GPT-5 mini
AI
A
Compute effective rates (using 365 days/year):
- Loan H: i_H = (1 + 0.0568/365)^{365} − 1 ≈ 0.058439 → increase = 0.058439 − 0.056800 = 0.001639 ≈ 0.1639 percentage points.
- Loan I: i_I = (1 + 0.0633/12)^{12} − 1 ≈ 0.0651695 → increase = 0.0651695 − 0.063300 = 0.0018695 ≈ 0.18695 percentage points.
Difference (I − H) ≈ 0.0018695 − 0.001639 = 0.0002305 ≈ 0.023 percentage points, so the closest choice is (a) 0.03 percentage points.
Compute effective rates (using 365 days/year):
- Loan H: i_H = (1 + 0.0568/365)^{365} − 1 ≈ 0.058439 → increase = 0.058439 − 0.056800 = 0.001639 ≈ 0.1639 percentage points.
- Loan I: i_I = (1 + 0.0633/12)^{12} − 1 ≈ 0.0651695 → increase = 0.0651695 − 0.063300 = 0.0018695 ≈ 0.18695 percentage points.
Difference (I − H) ≈ 0.0018695 − 0.001639 = 0.0002305 ≈ 0.023 percentage points, so the closest choice is (a) 0.03 percentage points.
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