Effective Annual Rate (EAR) Calculation for a Fixed-Rate Loan
How do you calculate the Effective Annual Rate (EAR) for a fixed-rate loan?
Given that you have agreed to a $40,000 fixed-rate loan from Chase Bank, with 36 equal monthly payments and an APR of 5.50%, what is the EAR of this loan?
Calculation of EAR for the Fixed-Rate Loan:
First, calculate the monthly payment using the loan amount and number of payments. Then, use the formula EAR = (1 + Monthly Interest Rate)^12 - 1. In this case, the EAR is 5.652384%.
To find the Effective Annual Rate (EAR) of a fixed-rate loan, we need to follow a few steps:
Step 1: Calculate the Monthly Interest Rate
Divide the APR by 12 to get the monthly interest rate. In this case, the monthly interest rate is 5.50% / 12 = 0.45833%.
Step 2: Determine the Monthly Payment
Calculate the monthly payment using the loan amount and the number of payments. The formula for the monthly payment of a fixed-rate loan is Monthly Payment = Loan Amount / Present Value Annuity Factor.
Using the loan amount of $40,000 and 36 payments:
- Calculate the Present Value Annuity Factor.
- Calculate the Monthly Payment using the formula.
Step 3: Calculate the Effective Annual Rate (EAR)
Once you have the monthly payment, use the formula EAR = (1 + Monthly Interest Rate)^12 - 1 to find the Effective Annual Rate.
After performing the calculations, the EAR of this loan is 5.652384%.