Question

A bank advertises an APR of 5.5% on personal loans. How much more is the APY when the rate is compounded monthly as compared to when it's compounded quarterly? Explain your answer.

Answer 1

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.

$APY=(1+\frac{r}{n})^n-1$, where,

r = Interest rate in decimal form,

n = Number of compounding periods per year.

Let us convert our given rate in decimal form.

$5.5\%=\frac{5.5}{100}=0.055$

Let us find APY, when the rate is compounded monthly by substituting n=12 and r=0.055 in APY formula.

$APY=(1+\frac{0.055}{12})^{12}-1$

$APY=(1+0.0045833)^{12}-1$

$APY=(1.0045833)^{12}-1$

$APY=1.05640786-1$

$APY=0.05640786$

$APY=0.05640786*100\approx 5.641\%$

Now let us find APY, when rate is compounded quarterly by substituting n=4 and r=0.055 in APY formula.

$APY=(1+\frac{0.055}{4})^4-1$

$APY=(1+0.01375)^4-1$

$APY=(1.01375)^4-1$

$APY=1.056144809-1$

$APY=0.056144809$

$APY=0.056144809[*100\approx 5.614\%$

Let us subtract APY when rate in compounded quarterly from APY, when rate is compounded monthly to find the difference.

$\text{The difference between APYs}= 5.641\%-5.614\%$

$\text{The difference between APYs}= 0.027\%$

Therefore, APY when the rate is compounded monthly is 0.027% greater than to APY, when the rate is compounded quarterly.