Question

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?

Answer 1

The correct answer for this question is:
The loan's effective rate that had the greater increase, relative to its nominal rate, and how much greater is its increase than that of the other loan is that 'loan H’s increase was 0.16 percentage points greater than Loan I’s.'

Here are the following choices:
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.

Answer 2

The loan with the greater increase in effective rate is loan I. It is greater by 0.19%.

What is effective rate?

Effective rate is the actual rate paid on a loan. It takes into account the effect of compounding.

Effective annual rate = (1 + APR / m ) ^m - 1

M = number of compounding

What are the effective rates of the loans?

Loan H = (1 + 0.0568/ 365)^365 - 1 = 5.84%

Loan I = (1 + 0.0633/12)^12 - 1 = 6.52%

What are the differences between effective rate and the nominal rates of the loans?

Loan H = 5.84 - 5.68 = 0.16%

Loan I = 6.52% -  6.33% = 0.19%

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