Frank is lending 1000 to Sarah for two years Frank and Sarah

Frank is lending $1,000 to Sarah for two years. Frank and Sarah agree that Frank should earn a 2 percent real return per year. Instructions: Enter your responses as integer values.

a. The CPI (times 100) is 100 at the time that Frank makes the loan. It is expected to be 110 in one year and 121 in two years. What nominal rate of interest should Frank charge Sarah? The nominal rate of interest charged should be ____________%.

b. Suppose Frank and Sarah are unsure what the CPI will be in two years. How should Frank index Sarah’s annual repayments to ensure that he gets an annual 2 percent real rate of return. Frank should charge Sarah _______% __less than or more than__the inflation rate.

Solution

a. Inflation is expected to be (110-100)/100 = 10% in the first year and (121-110)/110 = 10% in the second year. If Frank charges Sarah a 12% nominal interest rate, he will earn a real return of 2% per year (12% nominal interest rate – 10% inflation rate).

b. To ensure a 2% annual return on the loan, Frank and Sarah should agree that Sarah will pay an interest rate in each year equal to 2% plus whatever the inflation rate turns out to be. For example, if inflation turns out to be 8% during the first year and 10% during the second year, Sarah should pay 10% nominal interest in the first year and 12% in the second year.