Real and nominal rates interest Zane Perelli currently has $120 that he can spend today on polo shirts costing $ 30 each. Alternatively, he could invest the $120 in a risk-free U.S. Treasury security that is expected to earn a 13% 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.
a. To calculate how many polo shirts Zane can purchase today, we divide the amount Zane has ($120) by the cost of each polo shirt ($30).
Number of polo shirts = Amount available / Cost of each polo shirt
= $120 / $30
= 4 polo shirts
Therefore, Zane can purchase 4 polo shirts today.
b. Zane has the option to invest $120 in a risk-free U.S. Treasury security with a nominal interest rate of 13%. To calculate how much money Zane will have at the end of 1 year, we need to calculate the nominal interest earned.
Nominal Interest Earned = Initial investment * Nominal interest rate
= $120 * 13%
= $15.60
Zane will have $15.60 in interest at the end of 1 year. Adding this to the initial investment ($120), Zane will have a total of:
Total amount at the end of 1 year = Initial investment + Interest earned
= $120 + $15.60
= $135.60
Zane will have $135.60 at the end of 1 year if he forgoes purchasing the polo shirts today.
c. The consensus forecast of leading economists is a 4% rate of inflation over the coming year. To calculate the expected price of polo shirts at the end of 1 year, we need to calculate the inflation amount.
Inflation Amount = Initial price * Inflation rate
= $30 * 4%
= $1.20
The price of each polo shirt is expected to increase by $1.20. Therefore, the expected price of polo shirts at the end of 1 year will be:
Expected price = Initial price + Inflation amount
= $30 + $1.20
= $31.20
Polo shirts are expected to cost $31.20 at the end of 1 year in light of the expected inflation.
d. To determine how many polo shirts Zane can purchase at the end of 1 year, we divide the total amount Zane will have at the end of 1 year ($135.60) by the expected price of polo shirts ($31.20).
Number of polo shirts = Total amount at the end of 1 year / Expected price of polo shirts
= $135.60 / $31.20
≈ 4.348 polo shirts (rounded to 3 decimal places)
Therefore, Zane can purchase approximately 4.348 polo shirts at the end of 1 year. In percentage terms, we can find how many more or fewer polo shirts Zane can buy by calculating the percentage change.
Percentage Change = ((Number of polo shirts at the end of 1 year - Number of polo shirts today) / Number of polo shirts today) * 100
= ((4.348 - 4) / 4) * 100
= 8.7%
Zane can buy approximately 8.7% more polo shirts at the end of 1 year compared to today.
e. Zane's real rate of return over the year can be calculated by subtracting the inflation rate from the nominal interest rate.
Real Rate of Return = Nominal interest rate - Inflation rate
= 13% - 4%
= 9%
Zane's real rate of return over the year is 9%. The percentage change in Zane's buying power found in part d is also 8.7%.
The real rate of return and the percentage change in Zane's buying power are related because they both represent the increase in Zane's purchasing power. The real rate of return accounts for the effects of inflation, while the percentage change in buying power measures the difference in the number of goods Zane can purchase before and after inflation. Both indicate the increase in Zane's wealth in terms of real goods or the ability to buy more goods.