# Real Interest Rate Formula

## Formula

`r = (i - g)/(1 + g)`
Variables used in the annuity formula
r = Real interest rate
i = Nominal interest rate
g = Inflation rate

## Use

The real interest rate formula adjusts the nominal interest rate (i), for the effects of inflation (g) to calculate the real interest rate (r).

## Example 1: Using the Real Interest Rate Formula

If an amount is invested at an annual nominal rate of 5% and inflation is 3%, then the equivalent real interest rate is given as follows:

```Real interest rate formula = r = (i - g)/(1 + g)
i = 5%
g = 3%
Real interest rate = r = (5% - 3%)/(1 + 3%)
Real interest rate = r = 1.942%
```

## Example 2: Real Interest Rate Calculation

Suppose for example, 3,000 is invested in an account paying 6% interest and the rate of inflation was 2%. After a term of 5 years the future value of the amount adjusted for inflation, is given by the future value of a lump sum formula as follows:

```Real interest rate formula = r = (i - g)/(1 + g)
i = 6%
g = 2%
Real interest rate = r = (6% - 2%)/(1 + 2%)
Real interest rate = r = 3.9216%
FV = PV x (1 + r)^5
FV = 3000 x (1 + 3.9216%)^5
FV = 3,636.22
```

Notice that the real interest rate (r) was used in the future value formula as the future value adjusted for inflation was required. Of course the actual future value (the balance on the account), would be calculated using the nominal interest rate

## Fisher Real Interest Rate Equation

If inflation is low, then the real interest rate formula can be simplified to

`r = (i - g)`

The is known as the Fisher real interest rate equation, which states that when inflation is low, the real interest rate is approximately equal to the nominal interest rate less the inflation rate.

## Example 3: Using the Real Interest Rate Formula

If an amount is invested at an annual nominal rate of 7% and inflation is 1%, then the equivalent real interest rate is given as follows:

```Real interest rate formula = r = (i - g)/(1 + g)
i = 7%
g = 1%
Real interest rate = r = (7% - 1%)/(1 + 1%)
Real interest rate = r = 5.941%
Using the Fisher Equation
Fisher real interest rate equation = r = (i - g)
Real interest rate = r = (7% - 1%)
Real interest rate = r = 6%
```

In this case, as the inflation rate was low, the Fisher equation gives a good approximation (6%) compared to the real interest rate formula (5.941%).

The real interest rate formula is one example of an annuity formula used in time value of money calculations, discover another at the link below.

Real Interest Rate Formula November 6th, 2016

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