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? 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.

Answer 1

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

What is the effective rate?

The effective rate is also called the actual rate paid on a loan. It takes into account the effect of compounding.

Formula:

$\text{i}=(1+\dfrac{r}{m})^m-1$

Where, r = Nominal Rate,

m= number of compounding.

Computation of Effective interest rate:

The effective rate of interest of loan (H) is:

$\text{i}=(1+\dfrac{r}{m})^m-1\\\\\text{i}=(1+0.0568365)^3^6^5-1\\\\\text{i}=0.058439\\\\I=0.058439\times{100}\\I=5.8439\%$

The effective rate of interest of loan (I) is:

$\text{i}=(1+\dfrac{r}{m})^m-1\\\\\text{i}=(1+0.063312)^1^2-1\\\\\text{i}=0.065169\\\\I=0.065169\times{100}\\I=6.5169%$

The differences between the 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%

Therefore, the difference of interest of loan (I) is more than the loan (H) by 0.19%.

To learn more about the effective rate, refer to:

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