DEFINITION

Nominal interest rate refers to the rate of interest that does not consider the effects of inflation.
However, a positive rate of inflation would mean that the return earned is in fact much less.
So, the real interest rate refers to the interest rate after allowing for inflation. The real interest rate is less than the nominal interest rate when there is a positive rate of inflation.

**CALCULATOR**

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**FORMULA AND DERIVATION**

Let us suppose that an amount of \(\textrm{₹}1\) is deposited into a bank account that pays on interest of \(i\) p.a.
So, \(\textrm{₹}1\) would accumulate to \(1\left(1+i\right)\) at the end of the year. But this amount of \((1+i)\) is worth lesser due to the effects of inflation. Let us assume that the inflation is a constant rate \(j\). Then, the real worth of \((1+i)\) would be \({\left(1+i\right)}^1{\left(1+i\right)}^{\left(-1\right)}\) .
This is equivalent to accumulating \(\textrm{₹}1\) at rate \(i\) and discounting it at rate \(j\). This means that the real rate earned is not \(i\), but less than \(i\). So, if the real rate is \(i’\), then

\[1+i^{'}=\left(1+i\right){\left(1+i\right)}^{-1}\]
\[1+i^{'}=\frac{\left(1+i\right)}{\left(1+j\right)}\]
\[i^{'}=\frac{\left(1+i\right)}{\left(1+j\right)}-1\]
\[i^{'}=\frac{\left(i-j\right)}{\left(1+j\right)}\]

**EXAMPLES**

Example 1

Suppose, an amount of \(\textrm{₹}100\) was deposited into a bank that pays \(8\%\) p.a. interest. The rate of inflation was \(2.5\%\) p.a.

Here,

\(i=8\%\) p.a. and \(i=2.5\%\) p.a.

The real rate would be,

\[i^{'}=\frac{\left(i-j\right)}{\left(1+j\right)}\]
\[i^{'}=\frac{\left(0.08-0.025\right)}{\left(1.025\right)}\]
\[i^{'}=0.053658=5.366\%p.a.\]

So, the actual amount available in the bank account at the end of, say, 5 years would be
\(100\times {1.08}^{\left(5\right)}=146.93\) . But the effects of inflation would mean that this amount is worth less, in real. This is equivalent to accumulating the same \(\textrm{₹}100\) at real rate \(i’\). This would give us

\[{100\left(1+i^{'}\right)}^5=100\times {1.053658}^{\left(5\right)}=129.86\]

This means that the amount of \(\textrm{₹}146.93\) is only worth \(\textrm{₹}129.86\), due to inflation.