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. The real interest rate of an investment is calculated as the amount by which the nominal interest rate is higher than the inflation rate.

#### Real Interest Rate = Nominal Interest Rate – Inflation (Expected or Actual)

The real interest rate is the growth rate of purchasing power derived from an investment. By adjusting the nominal interest rate to compensate for inflation, you are keeping the purchasing power of a given level of capital constant over time.

For example, if you are earning 4% interest per year on the savings in your bank account, and inflation is currently 3% per year, then the real interest rate you are receiving is 1% (4% – 3% = 1%). The real value of your savings will only increase by 1% per year, when purchasing power is taken into consideration.

#### How to Calculate the Real Interest Rate?

For example let’s take the following data as the consumer price index (CPI) and nominal interest rate data:

CPI Data

- Year 1: 100
- Year 2: 110
- Year 3: 120
- Year 4: 115

Nominal Interest Rate Data

- Year 1: —
- Year 2: 15%
- Year 3: 13%
- Year 4: 8%

How can I calculate the real interest rate is for years 2, 3, and 4?

Notation

i: is the Inflation Rate

n: is the Nominal Interest Rate

r: is the Real Interest Rate

To calculate the real interest rate, we need to know the inflation rate or expected inflation rate, if we’re making a prediction about the future. From the data given we don’t have the inflation rate, but we can calculate it from the CPI data:

#### Calculating the Inflation Rate

We need to use the following formula:

i = [CPI(this year) – CPI(last year)] / CPI(last year).

So the inflation rate in year 2 is [110 – 100]/100 = .1 = 10%. We do this for all three years and get the following:

Inflation Rate Data

- Year 1: —
- Year 2: 10.0%
- Year 3: 9.1%
- Year 4: -4.2%

Now we can calculate the real interest rate. The relationship between the inflation

rate and the nominal and real interest rates is given by the expression: (1+r)=(1+n)/(1+i). However for low levels of inflation we can use the much simpler Fisher Equation to calculate the real interest rate:

#### FISHER EQUATION: r = n – i

Using this simple formula, we can calculate the real interest rate for years 2 through 4:

Real Interest Rate (r = n – i)

- Year 1: —
- Year 2: 15% – 10.0% = 5.0%
- Year 3: 13% – 9.1% = 3.9%
- Year 4: 8% – (-4.2%) = 12.2%

So the real interest rate is 5% in year 2, 3.9% in year 3, and a whopping 12.2% in year 4.

Final Interest Rate Data

Year / CPI / Nominal Interest Rate / Inflation Rate / Real Interest Rate

1 / 100 / — / — /–

2 /110 / 15% /10% /5%

3 / 120 / 13% / 9.1% /3.9%

4 / 115 / 8% / -4.2% /12.2%