Question

Real and nominal rates of interest Zane Perelli currently has $100 that he can spend today on socks costing $2.50 each. Alternatively, he could invest the $100 in a risk-free U.S. Treasury security that is expected to earn 9% nominal rate of interest. The consensus forecast of leading economist is a 5% rate of inflation over the coming year.

1. Number of Socks Zane Can Purchase today?

2. If Zane invests the money for 1 year he will have?

3. Expected cost of socks at the end of 1 year with expected inflation?

4. How many socks can Zane purchase at the end of 1 year?

5. In percentage terms, how many more or fewer socks can Zane buy at the end of year 1?

6. What is Zane's real rate of return over the year?

7. How is does the real rate of return relate to the percentage change in Zane's buying power fund in part d?

Answer 1

1. Number of socks Zane can purchase today = $100 / $2.5 = 40 socks

2. If Zane invests $100 for 1 year @9% interest he will have 100 * (1+.09)  = $109

3. Expected cost of socks at the at the end of 1 year with expected inflation = cost of socks * (1 + inflation rate)

= 2.5 * (1+0.05) = $2.625

4. Number of socks Zane can purchase at the end of 1 year = Amount available at the end of 1 year/ cost per socks at the end of 1 year   

    = 109 / 2.625 = 41.52 socks

5. Number of more or few socks Zain can buy at the end of 1 year = 41.52 - 40 = 1.52 more

In percentage terms it is = (41.52 - 40) / 40 * 100 = 3.8% more

6. Zane's real rate of return over the year = Nominal rate of return - inflation rate

= 9% - 5% = 4%

7. The 5% inflation rate over the year has increased the cost per socks from $2.5 to $2.625. If Zane invests $100 for 1 year @9% interest he will have $109 at the end of 1 year. The increase in amount at the end of the year is the nominal rate(9%) which must be reduced by the inflation rate(5%) to arrive at the real rate of return(4%). Zane's buying power therefore is reduced as real return(4%) is greater than the percentage increase in Zane's buying power which is 3.8%.