The real interest rate is currently 3%, and is expected to remain at that level

Question

The real interest rate is currently 3%, and is expected to remain at that level for the next two years. In contrast, the inflation premium is expected to increase from an annual rate of 2% during the next year, to an annual rate of 5% during the second year. A. What is the EXACT (3 decimal places) annual interest rate on a two-year loan? B. Assume that a fixed interest rate loan is issued at the rate you calculated in Part A. If the annual inflation rate turns out to be 2% over the entire two-year period (briefly explain each answer): • is purchasing power transferred from the borrower to the lender, or from the lender to the borrower? • is the realized real interest rate on this loan higher or lower than the expected real rate?

Explanation / Answer

interest rate in year 1 = 3% + 2% = 5%

interest rate in year 2 = 3% + 5% = 8%

a. annual interest rate of a two year loan = (1.05*1.08)^1/2 - 1 = 6.489%

b. since the borrower pays more in real terms, the purchasing power is transferred to the borrower

The realized real rate on this loan is higher since the inflation has dropped from an expectation of 5% to 2%

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