Question

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.

Answer 1

Loan U  will have a lower effective interest rate, and 0.0713 lower percentage points lower than Loan V and it can be determined by using the rate of interest formula.

Given that,

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.

We have to determine,

Which loan will have the lower effective interest rate, and how much lower will it be?

According to the question,

Effective Interest Rate;

The effective interest rate is determined by the formula;

$= \left(1+\dfrac{r}{t} \right )^t$

Loan U has a nominal interest rate of 9.97%,

Loan U is compounded daily,

Then,

The effective annual multiplier for loan U is,

$= \left(1+\dfrac{0.997}{365}\right)^{365}\\\\= (1+0.0027)^{365}\\\\= (1.0027)^{365}\\\\= 1.104824$

And Loan V has a nominal interest rate of 10.16%,

and Loan V is compounded quarterly.

Then,

$= \left(1+\dfrac{0.1016}{4}\right)^{4}\\\\= (1+0.0254)^{365}\\\\= (1.0254)^{365}\\\\= 1.105537$

Therefore,

Loan V has a higher effective rate by,

$=1.105537 -1.104824 \\\\= 0.000713 \\\\= 0.0713%$

Hence, Loan U  will have a lower effective interest rate, and 0.0713 lower percentage points lower than Loan V.

For more details about Interest rate refer to the link given below.

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