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:

1. Calculate the Present Value Annuity Factor.
2. 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%.