Mariq really likes M&Ms. Currently, he has $100, which, at the market price of $1 per bag of M&Ms, translates to 100 bags. He’s considering putting that money in the bank so next year he can afford even more M&Ms.

a. Suppose that Mariq can earn 7% interest on any money he saves. In one year, how many dollars will he have? How many M&Ms will he be able to afford?

b. The real rate of return is calculated by using goods and services rather than dollars. Calculate Mariq’s real rate of return by dividing next year’s possible M&M count by this year’s. In percentage terms, how many more M&Ms can Mariq enjoy?

c. Suppose Mariq can save at 7%, but that over the course of the year, the price of a bag of M&Ms increases by 3%, to $1.03. If Mariq saves his money today, how many bags of M&Ms will Mariq be able to afford next year? What is his real rate of return?

d. What happens to Mariq’s real rate of return if the price of a bag of M&Ms increases by 10%, to $1.10, over the next year?

e. Using your results from (b), (c), and (d), develop a formula that relates the nominal interest rate, the real interest rate, and the inflation rate (percentage increase in prices). Your formula may be an approximation.