Question

An investment currently pays 4% and the inflation rate is 1.5%. What is the exact real rate of interest?

Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit the % sign in your response. For example, an answer of 15.39% should be entered as 15.39.

Answer 1

Before coming to the question let us first take a look at some definitions-

1. Real Interest rate - A real interest rate is an interest rate that has been adjusted to remove the effects of inflation to reflect the real cost of funds to the borrower and the real yield to the lender or to an investor.

Also It can be described more formally described as the real interest rate is approximately the Nominal Interest rate minus the Inflation rate.

2. Nominal Interest rate – The nominal interest rate (also known as money interest rate) is the percentage increase in money you pay the lender for the use of the money you borrowed.

But the nominal interest rate doesn’t take inflation into account. In other words, it is unadjusted for inflation.

For example - Suppose the inflation at 7% this year Inflation is a rise in the general price level. A 7% inflation rate means that an average basket of goods you purchased this year is 7% more expensive when compared to last year. This leads to the concept of the real or inflation-adjusted interest rate.

Fisher equation

The relation between real and nominal interest rates and the expected inflation rate can be understood by the Fisher Equation -

(1 + i) = (1 + r) * (1 + x)

where,

i = nominal interest rate

r = real interest rate

x = expected inflation rate.

So for getting the real rate of interest the fisher equation can be modified as follows –

               [{(1 + i)/(1 + x)} – 1] * 100 = r

The calculations are as follows :

[{(1+0.04)/(1+0.015)} – 1] * 100 = r

Therefore real interest rate i.e. r = 2.46310

Nominal Inflation Adjusted Interest rate = 4%

Real Interest rate = 2.46310 Inflation = 1.5