Question

P6-3 Real and nominal rates of interest Zane Perelli currently has $100 that he can spend to- day 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 9% nominal rate of interest. The con- sensus forecast of leading economists is a 5% 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: c. How much would you expect the polo shirts ro cose 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 percent- age change in Zane's buying power found in part d? Explain.

Answer 1

As HOMEWORKLIB's policy, only the first four sub parts are answered.

Zane has $100

cost of polo shirt = $25

Sub part a:

Since Zane has $100 and one polo shirt costs $25, he can buy 100/25 = 4 shirts today

Sub part b:

Zane invests in risk free US treasury that earns 9% nominal interest.

Zane will have 100*(1+9%) at the end of the year = 100*(1+0.09) = 100(1.09) = $109

Sub part c:

Since inflation is 5%, the cost of all goods and services will go up by 5%.

Hence the cost of polo shirt will also grow by 5% to 25*(1+5%) = $26.25

Sub part d:

Zane has $109 at the end of the year and the polo shirt cost $26.25. Hence Zane will be able to buy 109/26.25 = 4.1524 shirts

in percentage terms it will be = (4.1524 - 4)/4 = 3.81%

Sub part e:

(1+nominal return) = (1+real return) *(1+inflation)

(1+real return) =  (1+nominal return) / (1+inflation) = (1+9%)/(1+5%) = 1.03809

hence real return = 1.03809 - 1 = 0.03809 = 3.81%

This is the same as Zane's buying power found in part d. Real return reflects the fact that inflation reduces the value of money over time. Hence nominal return itself is not sufficient to determine the buying power. one has to account for inflation to determine the real buying buying. This real buying buyer is depicted by real return.