Effective Annual Rate and Bank Selection for One-Year Investment

Explanation

The annual yield for Bank A is (1+10%/4)^4 - 1 = 10.38%, that for Bank B is 11% and that for Bank C is (1+10.5%/2)^2 - 1 = 10.78%. Therefore, you should invest with Bank B.

To determine the most advantageous bank to invest with for a one-year period and calculate the effective annual rate (EAR) for each bank, we need to compare the interest rates compounded differently.

1. Bank A offers an interest rate of 10% per year, compounded quarterly. This means that the interest is added to the principal amount every three months. To calculate the effective annual rate for Bank A, we can use the formula:

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

Where: r = annual interest rate (in decimal form) n = number of compounding periods per year

Substituting the values for Bank A: r = 10% = 0.10 n = 4 (quarterly compounding)

EAR for Bank A = (1 + (0.10/4))^4 - 1 = (1 + 0.025)^4 - 1 ≈ 10.38%

Therefore, the effective annual rate for Bank A is approximately 10.38%.

2. Bank B offers an interest rate of 11% per year, compounded annually. This means that the interest is added to the principal amount once per year. Since the interest is compounded annually, the EAR for Bank B is equal to the stated interest rate, which is 11%.

Therefore, the effective annual rate for Bank B is 11%.

3. Bank C offers an interest rate of 10.5% per year, compounded semi-annually. This means that the interest is added to the principal amount twice per year. Applying the same formula as before:

r = 10.5% = 0.105 n = 2 (semi-annual compounding)

EAR for Bank C = (1 + (0.105/2))^2 - 1 = (1 + 0.0525)^2 - 1 ≈ 12.01%

Therefore, the effective annual rate for Bank C is approximately 12.01%.

Comparing the effective annual rates, we can see that Bank B offers the highest effective annual rate of 11%. Therefore, the correct answer is:

A. Bank B, 11%