Question

(a) Define real interest rate. How is it related to nominal interest rate?

(b) Suppose the expected annual inflation rate in the U.S. is 1.5% and current nominal interest rate is 2%, what is the approximate real interest rate? What is the actual real interest rate?

Answer 1

a.

The real interest rate removes the effect of inflation and provides the real rate of interest of a loan or bond. Whereas the nominal interest rate is the interest rate on lending and borrowing transactions it doesn't adjust for the effect of inflation. The Fisher equation provides a relation between the nominal and real interest rates.

Approximate real interest rate  ≈ nominal interest rate − inflation rate

&

Actual real interest rate formula from Fisher equation is:

(1 + nominal interest rate) = (1 + real interest rate) (1 + inflation rate)

real interest rate = [(1 + nominal interest rate) / (1 + inflation rate)] -1

b.

expected annual inflation rate in the U.S. = 1.5%

current nominal interest rate i= 2%

approximate real interest rate = nominal interest rate − inflation rate = 2% - 1.5% = 0.5%

actual real interest rate = [(1 + nominal interest rate) / (1 + inflation rate)] -1

actual real interest rate = [(1+2%)/(1+1.5%)]-1

actual real interest rate = [(1+0.02)/(1+015)]-1

actual real interest rate = [1.02/1.015]-1

actual real interest rate = 1.004926 -1 = 0.004926 = 0.4926% = 0.49%

actual real interest rate is 0.49%