8/31/2019 Real Interest Rate Formula
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.
If the inflation rate is 3% per year, then the value of that coupon is 4% - 3% = 1%. In many cases, the real interest rates on savings accounts are negative. For instance, if a savings account pays 1.5% per year but inflation is 3%, the saver is effectively losing money every year he has the money in the account. Jan 6, 2019 - A nominal variable is one that doesn't incorporate the effects of inflation. A real variable factor in these effects. Find out how to calculate it.
Some Examples
For illustrative purposes, let's say that you've purchased a 1-year bond for face value that pays 6 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 6 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 3 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 6-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 over.
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 5 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 do it. 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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Real Rate of Return Formula (Table of Contents)
Real Rate of Return Formula
Real rate of return formula helps an investor find out what actually he gets in return for investing a specific sum of money in an investment.
For example, if Mr Timothy invests $1000 into a bank and bank promises to offer 5% rate of return, Mr Timothy may think that he is getting a good return on his investment. In financial terminology, we will call this 5% as nominal rate.
However, the question remains, is 5% the actual return on Mr Timothy’s investment? The answer is no. We also need to consider inflation and also tax (if the return on investment is not tax deductible).
By considering the inflation rate, we can calculate the real rate of return. Here’s the formula –
Example of Real Rate of Return Formula
Let’s take a simple example to illustrate the real rate of return formula.
You can download this Real Rate of Return Excel Template here – Real Rate of Return Excel Template
Ms. Soul has kept $100,000 in a bank. The bank promises to pay 6% rate of return at the end of the year. The inflation rate is 3% during the year. What would be the real rate of return?
By using the formula of real rate of return, we get –
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Explanation of Real Rate of Return Formula
Let’s look into the formula of the real rate of return.
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In this formula, we’re first considering the nominal rate and then we will consider the inflation rate.
As you already know – the rate of return on the investment or the bank offers is the nominal rate of return. However, to find out the inflation rate, we need to use the consumer price index. Alternatively, the businesses can use a different consumer price index to calculate the inflation or they can only take the goods and services into account that are related to their business.
Here’s the formula by using which we can find out the inflation rate –
Rate of Inflation = (CPI x+1 – CPI x) / CPI x
Here, CPI x means initial consumer index.
If you have invested a good amount, it’s always prudent to use the real rate of return to see how much you’re actually earning on the investment.
However, if you just want to make sure how much you’re actually making in a casual sense, you can just use the following formula – (nominal rate – inflation rate).
Though this formula is not recommended, you can just check before going into detail.
Use of Real Rate of Return Formula
As you can see already, the real rate of return is quite useful to the investors.
If the investors want to know how much they are actually making (in some cases it is actually negative), In this formula is a good one.
However, there are two things you need to consider before using this formula.
Real Rate of Return Calculator
You can use the following Real Rate of Return Calculator.
Real Rate of Return in Excel (with excel template)
Let us now do the same example above in Excel. This is very simple. You need to provide the two inputs of Nominal Rate and Inflation Rate.
You can easily calculate the real rate of return in the template provided.
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