Let 0 < r < 1 be an interest rate. Consider the following compound investment schemes:

Scheme I: Interest is compounded at a rate of r at the end of every month.

Scheme II: Interest is compounded at a rate of 3r at the end of every third month.

Scheme III: Interest is compounded at a rate of 6r at the end of every sixth month.

Question 1 Suppose that you invest R dollars on January 1st. Rank these three schemes in terms of which provides the greatest return after one year. Justify, using calculations and arguments, why you chose this ranking.

Question 2 Let rI, rII, and rIII denote the annual effective rates of the three schemes. Rank these three schemes in terms of their annual effective rates. Justify, using calculations and arguments, why you chose this ranking.