Which of the following interest rates would be preferred when taking out a loan?

When considering interest rates for a loan, it's important to recognize the implications of how frequently interest is compounded. The preference among these choices is based on the effective annual interest rate, which reflects the total amount of interest paid over a year based on the nominal interest and the frequency of compounding.

The choice of an annual interest rate at 4% signifies that the interest is applied once per year and does not change throughout the year. This makes it straightforward to calculate the cost of the loan and predict the total interest paid.

In contrast, a 4% interest rate that compounds quarterly or monthly leads to higher effective rates because interest is added to the principal more frequently. Thus, while the nominal rate might be the same (4%), the more frequent compounding would lead to a higher total cost of the loan over time. Similarly, a 5% monthly rate would incur even more interest than any of the 4% options, making it the least desirable choice.

Overall, the simplicity and lower effective interest rate of a 4% annual option make it the most desirable choice when taking out a loan.