Real and Nominal Interest Rates - Factoring in Inflation

Nominal interest rates are rates that have no inflation factored in. On the other hand, real interest rates are rates that have inflation already factored in. For example, suppose the current market inflation rate is 6% (meaning the cost of living is going up by 6% every year). And suppose an investment worth $100 today is worth $120 in 1 year. What is the rate of return on this investment?

The rate of return on this investment is $120 / 100 = 20% Since this 20% rate does not have inflation factored in, it is known as the Nominal Rate. On the other hand, what is the Real Interest Rate?

Real Interest Rate = Nominal Rate - Rate of Inflation

Therefore:

Real Interest Rate = 20% - 5%
Real Interest Rate = 15%

Another Example

Suppose you buy a bond for $100 that yields a coupon of 10% per year. At the end of the year, you have built up 1.1% x $100 = $110

Now suppose that inflation for the year is 5%. The basket of goods that you could buy for $100 last year would cost 1.05 x $100 = $105. Therefore:

Bond Coupon Yield = $110
Inflation Factored In = $105
Real Net Profit = $5

Calculating the Real Interest Rate

Question: Calculate Real Rate if Inflation is at 3% annually and nominal rate is 8%

Formula: (1 + Nominal) = (1 + Real Rate) x (1 + Inflation)

(1 + 0.08) = (1 + Real) x (1 + 0.03)
1 + Real = 1.08 / 1.03
1 + Real = 1.0485
Real Rate = 1.0485 - 1
Real Rate = 0.0485 or 4.85%