Respuesta :
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%
The difference between the interest is compounded daily, rather than compounded monthly is [tex]\boxed{0.0463{\text{ percentage}}}[/tex]. Option (d) is correct.
Further explanation:
Given:
Anna’s bank gives her a loan with a stated interest rate of [tex]10.22\%[/tex].
Explanation:
Anna’s bank gives her a loan with a stated interest rate of [tex]10.22\%.[/tex]
The difference between the effective interest rate be if the interest is compounded daily, rather than compounded monthly can be calculated as follows,
[tex]\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}[/tex]
The difference between the interest is compounded daily, rather than compounded monthly is [tex]\boxed{0.0463{\text{ percentage}}}[/tex]. 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.
