Question

First National Bank charges 11.7 percent compounded monthly on its business loans. First United Bank charges 11.9 percent compounded semiannually.

Answer 1

Answer:

a. EAR for First National Bank  = 12.35%

b. EAR for First United Bank = 12.25%

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

First National Bank charges 11.7 percent compounded monthly on its business loans. First United Bank charges 11.9 percent compounded semiannually.

Calculate the EAR for First National Bank and First United Bank. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation of the answers is now given as follows:

The effective annual rate (EAR) can be calculated using the following formula:

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

Where;

i = Annual interest rate of the bank

n = Number of compounding periods in a year

Therefore, we have:

a. Calculation of the EAR for First National Bank

i = Annual interest rate of First National Bank  = 11.7%, or 0.117

n = Number of compounding periods in a year = 12

Substituting the values into equation (1), we have:

EAR for First National Bank = ((1 + (0.117 / 12))^12) - 1

EAR for First National Bank = 1.12348257790079 - 1

EAR for First National Bank  = 0.12348257790079, or 12.348257790079%

Rounding to 2 decimal places as required, we have:

EAR for First National Bank  = 12.35%

b. Calculation of the EAR for First United Bank

i = Annual interest rate of First United Bank = 11.9%, or 0.119

n = Number of compounding periods in a year = 2

Substituting the values into equation (1), we have:

EAR for First United Bank = ((1 + (0.119 / 2))^2) - 1

EAR for First United Bank = 1.12254025 - 1

EAR for First United Bank = 0.12254025, or 12.254025%

Rounding to 2 decimal places as required, we have:

EAR for First United Bank = 12.25%