Verified Answer :
Answer:
20.7%.
Step-by-step explanation:
We have been given that Sam Seller offers credit at 19% interest per year.
We will annual percent yield formula to solve our given problem.
\(APY=(1+\frac{r}{n})^n-1\), where,
r = Interest rate in decimal form,
n = Number of times interest is compounded per year.
Let us convert our given interest rate in decimal form.
\(19\%=\frac{19}{100}=0.19\)
Upon substituting our given values in above formula we will get,
\(APY=(1+\frac{0.19}{12})^{12}-1\)
\(APY=(1+0.015833)^{12}-1\)
\(APY=(1.015833)^{12}-1\)
\(APY=1.207450998-1\)
\(APY=0.207450998\)
Let us convert APY in percentage by multiplying our answer by 100.
\(APY=0.207450998\times 100\)
\(APY=20.7450998\%\approx 20.7\%\)
Therefore, the APY is 20.7%.
Answer:
\(\text{APR}=20.7\%\)
Step-by-step explanation:
Given : Sam Seller offers credit at 19% interest per year.
To find : To the nearest tenth, APR ?
Solution :
The formula to calculate the annual percentage rate is given by
\(\text{APR}=(1+\dfrac{r}{n})^n-1\)
where, r is the interest rate i.e. r=19%=0.19
n is the number of time period for which interest is compounded per month i.e. n=12.
Substitute in the formula,
\(\text{APR}=(1+\dfrac{0.19}{12})^{12}-1\)
\(\text{APR}=(1+0.01583)^{12}-1\)
\(\text{APR}=(1.01583)^{12}-1\)
\(\text{APR}=1.2074-1\)
\(\text{APR}=0.2074\)
Into percentage,
\(\text{APR}=0.2074\times 100\)
\(\text{APR}=20.74\%\)
To the nearest tenth,
\(\text{APR}=20.7\%\)