# What is the total inflation rate over a several year period given the each year inflation rate?

Consider a given inflation rates $I_1, I_2, \dots, I_N$ for years $1 \dots N$. What is the total (cumulative) inflation rate over the whole period of $N$ years?

I was trying to chain-link the resulting purchasing powers: $P_1=P_0\frac{1}{1+I_1}$, $P_2=P_1\frac{1}{1+I_2}$, etc. yielding the $P_N=P_0\prod_{j=1}^{N}{\frac{1}{1+I_j}}$, but I cannot revert it back to inflation rate $I_1^N$.

EDIT1: Okay, I got the cumulative purchasing power rate: $P_1^N=\frac{P_N}{P_0}=\frac{1}{\prod_{j=1}^{N}{(1+I_j)}}$. I should express it in terms of cumulative inflation rate: $P_1^N=\frac{1}{1+I_1^N}$. Thus, $\frac{1}{1+I_1^N}=\frac{1}{\prod_{j=1}^{N}{(1+I_j)}}$, that is, $1+I_1^N = \prod_{j=1}^{N}{(1+I_j)}$, which gives $I_1^N = \prod_{j=1}^{N}{(1+I_j)} - 1$. Looks like an answer.

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It's just $(1+I_1)\cdots(1+I_N) - 1$. The ratio $P_0 / P_N$ of the purchasing powers gives you 1 + the rate of inflation for the whole period.