Question

Sam Seller offers credit at 19% interest per year. To the nearest tenth, APR =

Answer 1

`\text{APR}=20.7\%`

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+(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+(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* 100`

`\text{APR}=20.74\%`

To the nearest tenth,

`\text{APR}=20.7\%`

Answer 2

20.7%.

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+(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\%=(19)/(100)=0.19`

Upon substituting our given values in above formula we will get,

`APY=(1+(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* 100`

`APY=20.7450998\%\approx 20.7\%`

Therefore, the APY is 20.7%.