Calculating Effective Annual Interest Rate on Automobile Loan
What is the effective annual interest rate (EAR) on a \\( 6 \\% \\) APR automobile loan that has monthly payments?
The effective annual interest rate (EAR) on a 6% APR automobile loan with monthly payments is approximately 6.17%. To calculate the effective annual interest rate (EAR), we need to consider the compounding effect of monthly payments. The formula to calculate EAR is: EAR = (1 + r/n)ⁿ - 1 Where: r is the nominal interest rate (APR), and n is the number of compounding periods per year. In this case, the nominal interest rate is 6% APR, and since the loan has monthly payments, the compounding occurs monthly (n = 12). Plugging in the values, we have: EAR = (1 + 0.06/12)¹² - 1 ≈ 0.0617 or 6.17% Therefore, the effective annual interest rate (EAR) on the automobile loan is approximately 6.17%. So, the correct option is B.
Calculating Effective Annual Interest Rate
To calculate the effective annual interest rate on a loan, especially with compounding effects like monthly payments, we use the formula mentioned earlier: EAR = (1 + r/n)ⁿ - 1.Understanding the Formula Components:
- r: Nominal interest rate (APR) of the loan.
- n: Number of compounding periods per year, in this case, the loan has monthly payments (n = 12).
Calculation Steps:
- Calculate the monthly interest rate: r/n = 0.06/12 = 0.005.
- Raise (1 + r/n) to the power of n: (1 + 0.005)¹² = 1.0617.
- Subtract one from the result: 1.0617 - 1 = 0.0617 or 6.17%.
Therefore, by following these steps and calculations, we determine that the effective annual interest rate (EAR) on the automobile loan is approximately 6.17%.
For further information and examples on annual interest rates and calculations, you can refer to reliable finance resources.