Respuesta :
Answer:
0.027%
Step-by-step explanation:
We have been given that a bank advertises an APR of 5.5% on personal loans.
To solve our given problem we will Annual percentage yield formula.
[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,
r = Interest rate in decimal form,
n = Number of compounding periods per year.
Let us convert our given rate in decimal form.
[tex]5.5\%=\frac{5.5}{100}=0.055[/tex]
Let us find APY, when the rate is compounded monthly by substituting n=12 and r=0.055 in APY formula.
[tex]APY=(1+\frac{0.055}{12})^{12}-1[/tex]
[tex]APY=(1+0.0045833)^{12}-1[/tex]
[tex]APY=(1.0045833)^{12}-1[/tex]
[tex]APY=1.05640786-1[/tex]
[tex]APY=0.05640786[/tex]
[tex]APY=0.05640786*100\approx 5.641\%[/tex]
Now let us find APY, when rate is compounded quarterly by substituting n=4 and r=0.055 in APY formula.
[tex]APY=(1+\frac{0.055}{4})^4-1[/tex]
[tex]APY=(1+0.01375)^4-1[/tex]
[tex]APY=(1.01375)^4-1[/tex]
[tex]APY=1.056144809-1[/tex]
[tex]APY=0.056144809[/tex]
[tex]APY=0.056144809[*100\approx 5.614\%[/tex]
Let us subtract APY when rate in compounded quarterly from APY, when rate is compounded monthly to find the difference.
[tex]\text{The difference between APYs}= 5.641\%-5.614\%[/tex]
[tex]\text{The difference between APYs}= 0.027\%[/tex]
Therefore, APY when the rate is compounded monthly is 0.027% greater than to APY, when the rate is compounded quarterly.
The difference in the APY of the bank when there is monthly and quarterly compounding is 0.03%.
How to determine how much more the APY is?
In order to determine the difference in APY, the effective interest rate has to be determined. The effective interest rate is the real rate of borrowing. It takes into account compounding.
The formula used to calculate effective interest rate is = (1 + APR / m ) ^m - 1. Where M = number of compounding
Effective interest rate when there is a monthly compounding = (1 + 0.055/12)^12 - 1 = 5.64%
Effective interest rate when there is quarterly compounding = (1 + 0.055/4)^4 - 1 = 5.61%
Difference = 5.64 5.61 = 0.03%
To learn more about the effective annual rate, please check: https://brainly.com/question/4064975
