Question

Anna’s bank gives her a loan with a stated interest rate of 10. 22%. How much greater will Anna’s effective interest rate be if the interest is compounded daily, rather than compounded monthly? a. 0. 5389 percentage points b. 0. 1373 percentage points c. 0. 4926 percentage points d. 0. 0463 percentage points.

Answer 1

Anna's effective rate would be 0463 percentage greater than the interest is compounded daily, rather than compounded monthly.

The interest rate is given as 10. 22% or 0.1022 then the monthly effective rate would be:

$\text{Effective rate} = (1+(\frac{r}{m})^{m})$

$\text{Effective rate} = (1+(\frac{0.1022}{12})^{12})\\\text{Effective rate} = 1.10712576$

The daily effective interest rate would be:

$\text{Effective rate} = (1+(\frac{r}{m})^{m})$

$\text{Effective rate} = (1+(\frac{0.1022}{365})^{365})\\\text{Effective rate} = 1.107589126$

Hence, the difference in both rates of interest is calculated as:

$\text{Difference of rates} = \text{Daily effective rate} - \text{effective rate}\\\text{Difference of rates} = 1.107589126-1.10712576\\\text{Difference of rates}= 0.00046336$

Here, 0.00046336 would become 0.04634% when multiplied by 100.

Therefore, the correct option is d.

To know more about the calculation of the effective rates, refer to the link below:

https://brainly.com/question/24220522