Question

If Treasury bills are currently paying 4.1 percent and the inflation rate is 1.6 percent, what is the approximate and the exact real rate of interest? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

Approximate	%
Exact	%

Answer 1

Approximate real rate of interest is calculated as nominal rate of interest - rate of inflation.

Given that, nominal rate of interest=4.1%
Inflation rate=1.6%
Approximate real rate of interest=4.1%-1.6%=2.50%

Exact real rate of interest is calculated using the formula below:
(1 + nominal rate of interest) = (1 + real rate of interest)*(1 + expected rate of inflation)
=>(1 + real rate of interest)=(1 + nominal rate of interest)/(1 + expected rate of inflation)
=>Real rate of interest=(1 + nominal rate of interest)/(1 + expected rate of inflation) -1
Given that, nominal rate of interest=4.1%
Inflation rate=1.6%

So, exact real rate of interest=(1 + 4.1%)/(1 + 1.6%) -1
=(1.041/1.016)-1
=(1.024606299)-1
=0.024606299 or 2.46%