Question

Real and nominal rates interest   Zane Perelli currently has ​$100 that he can spend today on polo shirts costing $ 25 each. ​ Alternatively, he could invest the ​$100 in a​ risk-free U.S. Treasury security that is expected to earn a 12​% nominal rate of interest. The consensus forecast of leading economists is a 4​% rate of inflation over the coming year. a.  How many polo shirts can Zane purchase​ today?

b.  How much money will Zane have at the end of 1 year if he forgoes purchasing the polo shirts​ today? ​ (Ignore taxes.)

c.  How much would you expect the polo shirts to cost at the end of 1 year in light of the expected​ inflation?

d.  Use your findings in parts b and c to determine how many polo shirts​ (fractions are​ OK) Zane can purchase at the end of 1 year. In percentage​ terms, how many more or fewer polo shirts can Zane buy at the end of 1​ year?

e.  What is​ Zane's real rate of return over the​ year? How is it related to the percentage change in​ Zane's buying power found in part d​? Explain.

Answer 1

a. Zane has $100 with him. As each Polo shirt costs $25, hence 100/25 = 4. So Zane can purchase 4 polo shirts today.

b. The interest rate is 12% and hence on $100 Zane will earn (100*1*12)/100 = $12 in an year. So if Zane does not buy shirts and invests in the Treasury bills he wil get $112 = $100 + $12 = $112.

c. As the expected inflation is 4%, hence the cost of Polo shirt will increase by 4% in the next year. So that cost will be, $25 + (4*25)/100 = 25 + 1 = $26. Hence the Polo shirt will cost $26 after one year.

d. After one year Zane will have $112 with him and $26 is the cost of each Polo shirt. This is given Zane will invest the $100 into the Treasury bills. So, after one year, Zane will be able to buy 112/26 = 4.31 shirts.

e. Zane's real rate of return is 12% - 4% = 8%. Zane's buying power has increased by 8% due to the above calculation given which Zane can afford more shirts.