What Is The Effective Annual Interest Rate On A 9% Apr Automobile Loan That Has Monthly Payments?
To calculate the effective annual interest rate (EAR) on a loan with monthly payments, you can use the following formula, known as the Effective Annual Rate formula: EAR = ( 1 + 𝑟 𝑛 ) 𝑛 − 1 EAR = ( 1 + n r ) n − 1 Where: 𝑟 r is the nominal annual interest rate (APR) expressed as a decimal. 𝑛 n is the number of compounding periods per year. For a loan with monthly payments, the APR (nominal annual interest rate) is 9%, and since there are 12 months in a year, 𝑛 = 12 n = 12 . First, convert the APR from a percentage to a decimal: 𝑟 = 9 100 = 0.09 r = 100 9 = 0.09 . Then plug the values into the formula: EAR = ( 1 + 0.09 12 ) 12 − 1 EAR = ( 1 + 12 0.09 ) 12 − 1 EAR = ( 1 + 0.09 12 ) 12 − 1 EAR = ( 1 + 12 0.09 ) 12 − 1 EAR = ( 1 + 0.0075 ) 12 − 1 EAR = ( 1 + 0.0075 ) 12 − 1 EAR = ( 1.0075 ) 12 − 1 EAR = ( 1.0075 ) 12 − 1 EAR = 1.093806 − 1 EAR = 1.093806 − 1 EAR = 0.093806 EAR = 0.093806 To express the EAR as a percentage, multiply by 100: EAR = 0.093806 × 100 % EAR = 0.