P$6-7$ Nominal and real rates Paul loves to shop at Pound Place, where he can find many items priced at exactly $1.$ Paul has $300$ to spend and is thinking of going on a shopping spree at his favorite store, but he is also thinking of investing his money $1\mathrm{.}02.$

a$.$ Suppose the expected rate of inflation is $2\%($so next year, everything at Pound Place will cost $1\mathrm{.}02)$ and Paul can earn an annual interest of $6\%$ on his investments. Approximately what real rate of interest could Paul earn if he invests his money?

b$.$ How many items can Paul buy at Pound Place today, and how many can he buy a year from now if he invests today and goes shopping later? What is the percentage increase in Paul's purchasing power if he waits a year to shop? Compare your answer to the approximate real interest rate calculated in part a$.$

c$.$ Now suppose that the expected inflation rate is $8\%$ and Paul can earn $15\%$ annual interest on his investments. What is the approximate real rate of interest that Paul will earn? Calculate the number of items that Paul could buy next year from Pound Place if he invests his money. What is the percentage increase in his purchasing power if he waits a year to go shopping? Relate your answer back to Paul's real rate of return.