# Calculating and Understanding Real Interest Rates

Finance is riddled with terms that can make the uninitiated scratch their heads. "Real" variables and "nominal" variables are a good example. What's the difference? A nominal variable is one that doesn't incorporate or consider the effects of inflation. A real variable factors in these effects.

## Some Examples

For illustrative purposes, let's say that you've purchased a one-year bond for face value that pays six percent at the end of the year. You'd pay \$100 at the beginning of the year and get \$106 at the end because of that six percent rate, which is nominal because it doesn't account for inflation. When people speak of interest rates, they're typically talking about nominal rates.

So what happens if the inflation rate is three percent that year? You can buy a basket of goods today for \$100, or you can wait until next year when it will cost \$103. If you buy the bond in the above scenario with a six percent nominal interest rate, then sell it after a year for \$106 and buy a basket of goods for \$103, you'd have \$3 left.

## How to Calculate the Real Interest Rate

Start with the following 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 you figure out what the real interest rate is for years two, three, and four? Begin by identifying these notations: i means inflation rate, n is the nominal interest rate and r is the real interest rate.

You must know the inflation rate — or the expected inflation rate if you're making a prediction about the future. You can calculate this from the CPI data using the following formula:

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

So the inflation rate in year two is [110 – 100]/100 = .1 = 10%. If you do this for all three years, you'd get the following:

Inflation Rate Data

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

Now you 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), but you can use the much simpler Fisher Equation for lower levels of inflation.

FISHER EQUATION: r = n – i

Using this simple formula, you can calculate the real interest rate for years two through four.

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 percent in year 2, 3.9 percent in year 3, and a whopping 12.2 percent in year four.

## Is This Deal Good or Bad?

Let's say that you're offered the following deal: You lend \$200 to a friend at the beginning of year two and charge him the 15 percent nominal interest rate. He pays you \$230 at the end of year two.

Should you make this loan? You'll earn a real interest rate of five percent if you do. Five percent of \$200 is \$10, so you'll be financially ahead by making the deal, but this doesn’t necessarily mean you should. It depends on what's most important to you: Getting \$200 worth of goods at year two prices at the beginning of year two or getting \$210 worth of goods, also at year two prices, at the beginning of year three.

There's no right answer. It depends on how much you value consumption or happiness today compared to consumption or happiness one year from now. Economists refer to this as a person’s discount factor.

## The Bottom Line

If you know what the inflation rate is going to be, real interest rates can be a powerful tool in judging the value of an investment. They take into account how inflation erodes purchasing power.

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