Question

First National Bank charges 11.5 percent compounded monthly on its business loans. First United Bank charges 11.7 percent compounded semiannually. Calculate the Effective Annual Rate (EAR) for each bank.

Answer 1

To calculate the Effective Annual Rate (EAR), we use the formula EAR = (1 + (i / n))^n - 1. For First National Bank, the EAR is approximately 11.98535%. For First United Bank, the EAR is approximately 11.91225%.

Step-by-step explanation:

To calculate the Effective Annual Rate (EAR), we need to use the formula:

EAR = (1 + (i / n))^n - 1

Where i is the nominal interest rate and n is the number of compoundings per year.

For First National Bank:

i = 11.5% = 0.115 and n = 12 (compounded monthly).

Plugging these values into the formula:

EAR = (1 + (0.115 / 12))^12 - 1

EAR ≈ 0.1198535 or 11.98535%

For First United Bank:

i = 11.7% = 0.117 and n = 2 (compounded semiannually).

Plugging these values into the formula:

EAR = (1 + (0.117 / 2))^2 - 1

EAR ≈ 0.1191225 or 11.91225%