## It is fundamental to financial engineering that we understand the interplay between nominal and real terms due to inflation and its effect on such things as accounting for future expenses, asset growth or long-term investments.

The math behind adjusting for inflation is simple, but the underlying concept can quickly become confusing. Inflation represents increase in the price of everyday products and services we use or consume over time. Inflation erodes purchase power because one isn’t able to use one’s wealth to purchase nearly the same amount or kinds of products and services in the future as one is able to purchase in the present.

For example, consider the price of a loaf of bread; say it was \$0.5 100 years ago, costs \$5 today, and will be \$50 100 years into the future. Assume that the inflation rate remained constant at 2.3% a year.

There are two ways to represent inflation, in Nominal or Real terms. A nominal value represents the actual spot price of a product at a certain point in time, whether it is in the past or future. Naturally, as the price of this product increases due to inflation, its nominal value also increases. When the past or future product price is adjusted for inflation to reflect today’s price or the present value, it is said to be expressed in real terms. Hence, real value is always the same number.

So, how does one adjust for inflation? By using the good old compound interest rate formula discussed in detail in “Power of Compounding.” Let’s work out the numbers.

Nominal value of bread in 2120 = Today’s Price x (1 + Inflation Rate)Number of Years
= \$5 x (1+2.3%)100
≈ \$50

Real value of bread in 2120 = Spot Price / (1 + Inflation Rate)Number of Years
= \$50 / (1+2.3%)100
≈ \$5

Next, let’s review inflation-adjustment from a different perspective: asset growth. An investment of \$100 promises to yield a 10% return in one year. The expected account value at the end of the year is \$110. This is in nominal terms. Assuming a 2% inflation rate, the \$110 future value needs to be adjusted for inflation and expressed in today’s dollar value or in real terms. This is because, \$110 one year from now is only able to purchase 98% of goods and services compared to what it can buy today.

Real value can be calculated using one of two methods. The end balance can be discounted by the inflation rate using the compound interest formula we saw earlier. Alternatively, the growth rate can be reduced by the inflation rate. When using an inflation-adjusted return, the end balance will be in real terms. The expression of investment value in real terms makes it possible to compare investment returns with different holding periods. The article “Effect of Taxes vs. Inflation on Asset Growth” delves deeper into this topic.

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