# Real Interest Rate Calculator

Created by Krishna Nelaturu
Last updated: Jul 05, 2022

Our real interest rate calculator can help you find the real interest rate by adjusting the nominal interest rate to the inflation rate. Keep scrolling to learn more about the real interest rate. Specifically, we shall take a close look at:

• What are the real and nominal interest rates? How are they affected by inflation?
• How do you find the real interest rate with the nominal and inflation rate?
• What is the after-tax real interest rate formula?

If you're exclusively interested in calculating how your investment or loan compounds over time, use our compound interest calculator.

## Real interest rate, nominal interest rate, and the effects of inflation

In finance, money in your hands today is worth more than the same amount in your hands at a later time. We call this concept the time value of money. This loss in the money's worth does not include inflation, which is a general rise in the prices of goods and services with time.

When a person (or an institution) lends someone money (or invests in a venture), they charge an interest rate to make up for the lost time value of money, expected inflation, and other losses in the of the repaid amount. We call this interest rate the nominal interest rate. Learn how it effects your loans through our loan calculator.

However, the true interest someone earns on their investment is subject to the actual inflation during the period of investment (or lending). Adjusting the nominal interest rate to reflect the actual inflation will give the investor the real interest rate they've earned on their investment. We call this adjusted interest rate the real interest rate.

🔎 An investor can also use the real interest rate to determine how much nominal interest rate they should charge by adding the effects of the expected inflation rate. We shall learn how to do this in the next section using the real interest rate equation.

## Fisher equation: How do you calculate the real interest rate?

The Fisher equation gives the relationship between the nominal and real interest rates and the rate of inflation:

$1 + i = (1+r)(1+\pi_e)$

where:

• $i$ - The nominal rate of interest;
• $r$ - The real interest rate; and
• $\pi_e$ - The expected inflation rate.

Rearranging this Fisher equation, we get the real interest rate formula:

\begin{align*} 1+r &= \frac{1+i}{1+\pi_e}\\ r &= \frac{1+i}{1+\pi_e}-1\\ r&= \frac{i-\pi_e}{1+\pi_e} \end{align*}

For cases where the inflation and the nominal interest rates are relatively low, we can approximate the real interest rate using:

$r = i- \pi_e$

This real interest rate equation is how you find the real interest rate with nominal and inflation rates.

Let's learn how to calculate real interest rate with an example. Consider the case where the nominal interest rate is $i=7 \%$ and the inflation rate is $\pi_e=3.5 \%$. Using the real interest rate formula:

\begin{align*} r&= \frac{7\%-3.5\%}{1+3.5\%}\\[1em] &= \frac{\frac{7-3.5}{100}}{\frac{100+3.5}{100}}\\[1em] &= \frac{3.5}{103.5}\\[1em] r &= 0.033816 = 3.382\% \end{align*}

The approximate rate of interest would be:

$r = 7\% - 3.5\% = 3.5\%$

## What is the formula for after-tax real interest rate?

If the interest earnings are taxable, the investor earns even lower real interest than we saw in the previous section. The formula for after-tax real interest rate is:

$r_{\text{taxed}} = i(1-t) - \pi_e$

where:

• $r_{\text{taxed}}$ - The after-tax real interest rate;
• $i$ - The nominal interest rate before-tax;
• $t$ - The amount of tax per dollar (or any currency invested); and
• $\pi_e$ - The expected inflation rate.

## How to use this real interest rate calculator?

You can use this versatile real interest rate calculator to find out the real interest rate:

1. Enter the nominal interest rate.
2. Provide the expected inflation rate.
3. The calculator will instantly give you both the real interest rate and an approximate real interest rate.
4. If the interest is taxable, click the Advanced mode button at the bottom left and enter the tax per dollar as a percentage. The calculator will further adjust the real interest rate to reflect the taxed amount.

You can also use it backward, to determine the nominal interest rate or the expected inflation from the real interest rate.

Krishna Nelaturu
Nominal interest rate (i)
%
Expected inflation rate (πₑ)
%
Real interest rate (r)
%
Approximate real interest rate
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