calculate the effective yield, then rank them from highest yield to lowest yield:
12% compound annually
11.8% compound quarterly
11.9% compound semiannually
To calculate the effective yield, we need to convert each of the given interest rates into their effective annual rates.
For the first option, 12% compound annually, the effective annual rate is simply 12%.
For the second option, 11.8% compound quarterly, we need to calculate the effective annual rate using the formula:
Effective Annual Rate = (1 + (interest rate / number of compounding periods))^number of compounding periods - 1
Using this formula, the effective annual rate for 11.8% compound quarterly is:
Effective Annual Rate = (1 + (0.118 / 4))^4 - 1 = 12.1175%
For the third option, 11.9% compound semiannually, we use the same formula:
Effective Annual Rate = (1 + (0.119 / 2))^2 - 1 = 12.0225%
Now that we have calculated the effective annual rates for each option, we can rank them from highest to lowest yield:
1. 11.8% compound quarterly - Effective annual rate: 12.1175%
2. 11.9% compound semiannually - Effective annual rate: 12.0225%
3. 12% compound annually - Effective annual rate: 12%
Therefore, the ranking from highest to lowest yield is as follows:
1. 11.8% compound quarterly
2. 11.9% compound semiannually
3. 12% compound annually