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 t

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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 t

he 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

Mathematics

2 answers:

Cerrena [4.2K] · Answer 1 · 2022-02-16T10:28:21+03:00

The difference between the interest is compounded daily, rather than compounded monthly is $\boxed{0.0463{\text{ percentage}}}$ . Option (d) is correct.

Further explanation:

Given:

Anna’s bank gives her a loan with a stated interest rate of $10.22\%$ .

Explanation:

Anna’s bank gives her a loan with a stated interest rate of $10.22\%.$

The difference between the effective interest rate be if the interest is compounded daily, rather than compounded monthly can be calculated as follows,

$\begin{aligned}{\text{Difference}} &= {\left( {1 + \frac{{0.1022}}{{365}}} \right)^{365}} - {\left( {1 + \frac{{0.1022}}{{12}}} \right)^{12}}\\&= 1.107589 - 1.107126\\&= 0.000463\\&= 0.0463\%\\\end{aligned}$

The difference between the interest is compounded daily, rather than compounded monthly is $\boxed{0.0463{\text{ percentage}}}$ . Option (d) is correct.

Option (a) is not correct.

Option (b) is not correct.

Option (c) is not correct.

Option (d) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Simple interest

Keywords: nominal rate, compounded daily, effective rate, compounded monthly, Anna’s bank, Anna, bank, loan, percentage, interest rate, Principal, invested, interest rate, account, effective interest rate, total interest, amount.