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

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.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

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.

Answer 2

Original APR = 10.22% compounded monthly.

Original effective interest rate, compounded monthly

= (1+(0.1022/12))^12

= 1.10712576

Original effective interest rate, compounded daily

= (1+(0.1022/365)^365

= 1.107589126

Difference in rate due to compounding periods

= 1.107589126 -  1.10712576

= 0.00046336

= 0.04634%