Final answer:
After computing the effective annual rate for both loan options, the loan with 20% interest compounded monthly has an EAR of 21.939% and is found to be the more attractive option compared to the 22% loan compounded annually.
Step-by-step explanation:
To determine which loan alternative is more attractive, we need to compare the effective annual rates (EARs) for both loans. The formula to calculate EAR is (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1. For the 22% loan compounded annually, the EAR is simply 22%, since it compounds once per year. However, for the 20% loan compounded monthly, the calculation is a bit more complex: (1 + (0.20 / 12))^12 - 1.
Let's compute the EAR for the second option: (1 + (0.20 / 12))^12 - 1 = (1 + 0.0167)^12 - 1 = 1.21939 - 1 = 0.21939, which is 21.939% when expressed as a percentage. Now, comparing the EAR of both loans: 22.00% (annually compounded) and 21.939% (monthly compounded), we can see that the loan with 20% interest rate compounded monthly effectively has a lower annual rate and is therefore the more attractive option.