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

Divide the investment’s future nominal value by the compounded inflation factor. For annual interest rate $i$, annual inflation rate $r$, initial investment $P$, and $n$ years, the real value is

$$V_{\text{real}}=\frac{P(1+i)^n}{(1+r)^n}=P\left(\frac{1+i}{1+r}\right)^n.$$

Why This Works

The nominal value is the amount shown in the account after interest has been added. However, inflation reduces the purchasing power of that money.

The fraction $\frac{1+i}{1+r}$ is the annual real growth factor. A value greater than $1$ means purchasing power increases, while a value below $1$ means it decreases. This factor must be compounded for the full investment period.

If interest and inflation are equal, the real growth factor is exactly $1$, so purchasing power is unchanged. If inflation is higher, the nominal balance may still rise while its real value falls. For example, $4\%$ interest and $6\%$ inflation give a real growth factor of $\frac{1.04}{1.06}\approx0.981$, representing about a annual loss in purchasing power.

Suppose \10,000$is invested for four years at$5%$annualcompoundinterestwhileinflati$3%$ per year.

First calculate the nominal value:

$$V_{\text{nominal}}=10\,000(1.05)^4=\$12\,155.06.$$

Then adjust for inflation:

$$V_{\text{real}}=\frac{12\,155.06}{(1.03)^4}=\$10\,799.61.$$

Therefore, although the account contains \12,155.06$, it has the same purchasing power as approximately$$10,799.61$ today. The investment has increased in real terms because the interest rate exceeds inflation.

The exact annual real growth rate is

$$\frac{1.05}{1.03}-1=0.0194=1.94\%.$$

This is slightly less than the approximate rate $5\%-3\%=2\%$. A common misconception is to subtract inflation directly from the final balance or use the rate difference as an exact result; both rates compound.

Exam Technique

This is SL 1.4 Financial applications. Show nominal growth and the inflation adjustment separately, retain full GDC precision, and give money to two decimal places. If asked to interpret, explain what the result means for purchasing power.