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 if compounded daily, rather than compounded monthly.

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

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

The daily effective interest rate would be:

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

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

$1.107589126 - 1.10712576\\= 0.00046336$

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

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