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Real and nominal rates interest Zane Perelli currently has $116 that he can spend today on socks costing $2.90 each. Alternatively, he could invest the $116 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 5% rate of inflation over the coming year. a. How many socks can Zane purchase today? b. How much money will Zane have at the end of 1 year if he forgoes purchasing the socks today and invests his money instead? (Ignore taxes.) c. How much would you expect the socks 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 socks (fractions are OK) Zane can purchase at the end of 1 year. In percentage terms, how many more or fewer socks can Zane buy at the end of 1 year? e. What is Zanes real rate of return over the year? How is it related to the percentage change in Zanes buying power found in part d? Explain.

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Answer #1

Calculate the amounts, units and real rate of return as follows:

1 a Particulars 2 Current amount 3 Stock cost 4 Stocks purchased Amount 116 2.9 40 6 b Nominal rate 12% 129.92 7 Future value 9 c Inflation rate 10 Future value of stock cost 5% 3.045 12 d Stocks 13 14 15 e Nominal rate 16 Inflation rate 17 Real rate 18 If funds are invested its buying power will 42.67 6.67% % change 12.00% 5. 00% 6.67% increase, if they are kept ideal buying power decrease due to increase in inflation. 19

Formulas 1 a Particulars 2 Current amount 3 Stock cost 4 Stocks purchased Amount 116 2.9 -C2/C3 6 b Nominal rate 7 Future value 0.12 C2* (1+C6) 9 c Inflation rate 0.05 10 Future value of stock cost C3*(1+C9) -C7/C10 (C12-C4)/C4 12 d Stocks 13 %change 14 15 e EB6 16 B9 17 Real rate 18 -C6 C9 -((1+C15)/(1+C16))-1 If funds are invested its buying power will increase, if they are kept ideal buying power decrease due to increase in inflation 19

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