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

The effective rate of interest is the real return on a savings account when the effects of an increase over time are taken. Loan U having a lower by 0.000713 points lower than Loan V.

What is the effective rate of interest?

The effective interest rate is also known as the effective annual interest rate, It is the interest rate on a loan and is shown as the equivalent interest rate if compound interest was payable annually in liabilities.

Computation of the effective rate of interest:

The formula of effective rate of interest is:

$(1+\frac{r}{t} )t$

For Loan U:

Nominal rate = 10.16% and compounded daily.

Now by putting the values in the above formula, we get,

$=(1+\frac{r}{t} )^t\\\\=(1+\frac{0.997}{365} )^3^6^5\\\\=(1+0.0027)^3^6^5\\\\=1.104824$

For loan V:

Nominal rate = 10.16% and compounded quarterly.

Now by putting the values in the above formula, we get,

$=(1+\frac{r}{t} )^t\\\\=(1+\frac{0.1016}{4} )^4\\\\=(1+0.0254)^4\\\\=1.105537$

Therefore, Loan V has a greater effective interest rate to be 0.000713 (1.105537-1.104824).

To learn more about the effective rate of interest, refer to:

brainly.com/question/14270693