Question

Inflation, nominal interest​ rates, and real rates. From 1991 to​ 2000, the U.S. economy had an annual inflation rate of around 2.17​%. The historical annual nominal​ risk-free rate for this same period was around 4.96​%. Using the approximate nominal interest rate equation and the true nominal interest rate​ equation, compute the real interest rate for that decade.

What is the estimated real interest rate using the approximate nominal interest rate equation for that​ decade?

________​(Round to two decimal​ places.)

What is the true annual real interest rate using the true nominal interest rate equation for that​ decade?

________​(Round to two decimal​ places.)

Answer 1

The real rate of interest is an inflation adjusted interest rate so the easiest way to calculate an estimated value of real rate of interest is:

Where is real rate of interest, i is nominal rate of interest and i.r is inflation rate.

Therefore, according to this problem,

= 4.96% -2.17% = 2.79%

So the estimated value is 2.79%

While this is an estimation, the true value can be determined with the following equation:

So, the true annual real rate of interest is

(1+ ) = (1+0.0497)/(1+0.0219)

= 1.0272 - 1

= 0.0272 i.e. 2.72%