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5 Jul 2019

1) The expected inflation rate over the next year is 2%. You see that the posted one-year interest rate on government bonds (no default risk) is 5%. What is the (ex-ante) real interest rate?

2) Inflation turns out to be 1%. What is the (ex-post) real interest rate that the borrow paid/lender received?

3) Who benefited from the drop in inflation? 

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Related questions

Suppose I borrow $200,000 for one year at a fixed nominal interest rate of 7 percent.

(a) What is my nominal repayment next year?

(b) Suppose that at the time the loan was made, both the lender and I believed that the (ex-ante) rel interest rate on the loan would be two percent. Suppose the actual inflation rate over the life of the loan turns out to be 4 percent. What is the ex-post real interest rate? Does the inflation rate help me at the expense of the lender, or help the lender at my expense?

(c) Re-do question (b) assuming that the inflation rate turns out to be 5 percent and 6 percent.

(d) Given that the lender and I agreed that the ex-ante real interest rate should be 2 percent, what nominal interest rate would I have been charged if the lender and I had expected inflation over the life of the loan to be 10 percent? 3 percent? 0 percent?

(e) Inflation increased enexpectedly during the 1970s. Explain why this helped someone who bought a house using a 30-year mortgage with fixed nominal interest rates in 1965, but not someone who bought a house using a 30-year mortgage with a fixed nominal interest rate in 1980.

1. Nominal and real interest rates: 

a. Explain the difference between real and nominal interest rates. 

b. Which of these two interest rates is relevant for investment and consumption decisions and why? 

c. How is the real interest rate calculated ex-post? How is the real interest rate calculated ex-ante? 

 

2. Fisher parity

a. Write down the approximation formula of the Fisher parity.

b. What is the real interest rate if the nominal interest rate is 6% and the expected inflation rate is 1%?

c. How is the real interest rate affected if the expected inflation increases while the nominal interest rate remains constant?

d. Given that the nominal interest rate can’t be negative ("zero lower bound"), what is the lowest value the real interest rate can be?

Suppose John borrows $100 from Jane for one year at a fixed nominal interest rate. Suppose John and Jane both agree that the ex-ante real interest rate on the loan should be 3%.

a) What will be the nominal interest rate on the loan according to the Fisher Equation, if the expected inflation rate over the next year is:

5 percent? 3 percent? 0 percent? -2 percent? -4 percent? -6 percent?

b) If there is a zero lower bound on interest rates, what will the nominal interest rate actually be when expected inflation is equal to:

-4 percent or -6 percent?

What will the ex-ante real interest rate be in those cases?

c) Explain why deflation can be disruptive to credit markets and the economy (which is why monetary policymakers try to avoid deflation by making sure the money supply grows over time).

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