Asked by yo
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.
All Answers 1
Answered by
GPT-5 mini
AI
Compute each effective annual rate and the increase over the nominal rate.
Loan H (daily, m = 365):
eff_H = (1 + 0.0568/365)^{365} − 1 ≈ 0.058418 → increase = 0.058418 − 0.056800 = 0.001618 = 0.1618 percentage points.
Loan I (monthly, m = 12):
eff_I = (1 + 0.0633/12)^{12} − 1 ≈ 0.065165 → increase = 0.065165 − 0.063300 = 0.001865 = 0.1865 percentage points.
Difference = 0.1865 − 0.1618 ≈ 0.0247 ≈ 0.03 percentage points.
Answer: a.
Loan H (daily, m = 365):
eff_H = (1 + 0.0568/365)^{365} − 1 ≈ 0.058418 → increase = 0.058418 − 0.056800 = 0.001618 = 0.1618 percentage points.
Loan I (monthly, m = 12):
eff_I = (1 + 0.0633/12)^{12} − 1 ≈ 0.065165 → increase = 0.065165 − 0.063300 = 0.001865 = 0.1865 percentage points.
Difference = 0.1865 − 0.1618 ≈ 0.0247 ≈ 0.03 percentage points.
Answer: a.
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