Inflation over Several Years

When calculating inflation overs several years you have to multiply values as prices are increasing from a new base each time. E.g., if in first year inflation was 3% and in the second 5%, then over two years inflation was $(1+0.03)\times (1+0.05)=1.0815-1=0.0815$, so 8.15%. Similarly, average inflation is computed as a geometric mean, and for this example will be $\sqrt{(1.03\times 1.05)}-1=1.0399-1=0.0399$, so 3.99%. Geometric mean is usually less than arithmetic mean, being equal only when all values are the same. Multiyear inflation is larger than sum of annual inflations. In general, if with have inflation over $n$ years as $i_1..i_n$, the total inflation will be:

If inflation is constant for all years, then this is simplified to ${(1+i)}^n-1$. Similarly, if $I$ is inflation over $n$ years, then average annual inflation is $\sqrt[n]{1+I}-1$.

For example, if you have $100 today, and inflation is 3.2% annually, you’d need $137.02 in 10 years to have the same purchasing power. If your net worth is not growing faster than that, you are losing money. $100,000 left uninvested loses $\$100,000-\frac{\$100,000}{1.032}=\$3,100$ in the first year alone; in 10 years it would be worth just $\frac{\$100,000}{{(1+0.032)}^{10}}=\$72,982$ in today’s dollars.