How Do Interest Rate and Inflation Affect the Real Value of an Investment?

An investment’s real value increases only when its growth after interest exceeds the loss of purchasing power caused by inflation. If inflation is greater than the interest rate, the investment may grow in nominal terms while falling in real value.

The Mechanism

The nominal value is the amount shown in the account. For an initial investment of $P$, annual interest rate $i$, and investment period $n$,

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

To express this future amount in today’s purchasing power, divide by the cumulative effect of inflation, where $\pi$ is the annual inflation rate:

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

The exact real rate of return is therefore

$$r=\frac{1+i}{1+\pi}-1.$$

For small rates, $r\approx i-\pi$, but this subtraction is only an approximation.

This distinction matters because inflation compounds just as interest does. Each year, the account balance is multiplied by $1+i$, while the purchasing-power adjustment is multiplied by $1+\pi$. Consequently, comparing $i$ and $\pi$ identifies the direction of change, but the ratio gives the exact size of the real return.

Worked Example

Suppose \text{\}10,000$is invested for five years at$5%$annual interest while inflation is$3%$.

$$FV=10\,000(1.05)^5=\text{\$}12\,762.82.$$

However, its real value is

$$\frac{12\,762.82}{(1.03)^5}=\text{\$}11\,009.57.$$

The account grows by $27.6\%$ nominally, but its purchasing power grows by only about $10.1\%$. Here, the real annual growth factor is $\frac{1.05}{1.03}\approx 1.01942$, so the exact annual real return is about , not . Compounding this factor for five years produces the real increase.

A common misconception is that any positive interest rate makes an investor wealthier. This is false because inflation may rise faster than the investment.

IB Exam Technique

For SL 1.4, financial applications, first use the GDC finance solver to find the future value, keeping full precision. Then deflate that value by $(1+\pi)^n$, round money to two decimal places, and interpret whether purchasing power increased or decreased.