How Do You Find the Real Value of an Investment Accounting for Inflation?

Divide the investment’s nominal value by the accumulated inflation factor. If the investment and inflation both compound annually, the real value after $n$ years is

$$\text{Real value}=P\left(\frac{1+i}{1+j}\right)^n,$$

where $P$ is the initial investment, $i$ is the annual investment return, and $j$ is the annual inflation rate.

This is part of IB Mathematics: Analysis and Approaches, SL 1.4: Financial applications and applies to both AA SL and HL students.

Why This Works

The investment first grows in nominal terms:

$$A=P(1+i)^n.$$

However, prices also grow because of inflation. After $n$ years, the inflation factor is $(1+j)^n$. Dividing nominal wealth by this factor expresses the investment in today’s purchasing power:

$$\text{Real value}=\frac{P(1+i)^n}{(1+j)^n}.$$

For example, suppose P=\text{\}10{,}000$, the annual return is$5%$, inflation is$2%$, and the investment lasts three years.

First calculate the nominal value:

$$A=10{,}000(1.05)^3=11{,}576.25.$$

Then adjust for inflation:

$$\text{Real value}=\frac{11{,}576.25}{(1.02)^3}=10{,}908.4.$$

Therefore, the investment is worth approximately \text{\}10{,}908$in today’s money. Its nominal gain is$\text{$}1{,}576.25$,butitsrealgainiso$\text{$}908$.

A common misconception is to subtract inflation directly from the final balance. Inflation is a compound percentage change, so you must divide by the accumulated inflation factor. Also, (i-j) is only an approximation to the real return; the exact periodic real rate is $\frac{1+i}{1+j}-1$.

Interpreting the Result

An exact real growth factor is useful for interpretation. Here, each year’s purchasing power is multiplied by $1.05/1.02$, not by $1+0.05-0.02$. Thus, the exact annual real return is about $2.94\%$. Because this factor exceeds $1$, purchasing power rises; if it equals $1$, purchasing power is unchanged; and if it is below , the investment grows nominally but loses real value. Match the compounding period used for both rates.

Exam Technique

For the command term calculate, show the nominal-value calculation and the inflation adjustment before giving the final answer. This is usually suited to Paper 2 because a GDC or financial application may be required; round as instructed, or otherwise give three significant figures.