Respuesta :
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;
[tex]= \left(1+\dfrac{r}{t} \right )^t[/tex]
Loan U has a nominal interest rate of 9.97%,
Loan U is compounded daily,
Then,
The effective annual multiplier for loan U is,
[tex]= \left(1+\dfrac{0.997}{365}\right)^{365}\\\\= (1+0.0027)^{365}\\\\= (1.0027)^{365}\\\\= 1.104824[/tex]
And Loan V has a nominal interest rate of 10.16%,
and Loan V is compounded quarterly.
Then,
[tex]= \left(1+\dfrac{0.1016}{4}\right)^{4}\\\\= (1+0.0254)^{365}\\\\= (1.0254)^{365}\\\\= 1.105537[/tex]
Therefore,
Loan V has a higher effective rate by,
[tex]=1.105537 -1.104824 \\\\= 0.000713 \\\\= 0.0713%[/tex]
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.
https://brainly.com/question/1398822
