Question

You have just taken out a $2,650 loan from your local bank. You paid off the loan in 1 year by making 12 monthly payments with a total interest charge of $300.00. Determine, from the information given, the annual percentage rate (APR). Round your answer to the nearest hundredth of a percent.

Answer 1

20.33%

Explanation:

Principal = $2650

Total Interest = $300

Total amount = 42650+$300=$2950

Since we are given that You paid off the loan in 1 year by making 12 monthly payments

So, monthly payment =
`(2950)/(12) =245.833`

Formula of monthly payment =
`\text{Monthly payment }= (Principal * (i)/(12))/(1-(1+(i)/(12))^(-12))`

where i is the rate of interest in decimals

To find i substitute the values

`245.833= (2650 * (i)/(12))/(1-(1+(i)/(12))^(-12))`

using calculator

`i=0.2033`

So, rate of interest in percent =
`0.2033 * 100 = 20.33\%`

Thus the annual percentage rate (APR) is 20.33%