Cost-of-living index

Statement

If the cost of living rises by $10\%$ each year starting from an index of $100$ in $2020$, what will the index be in $2026$?

Solution

From $2020$ to $2026$ is $6$ years: $C=100\,(1{.}10)^{6}$. $C=100\cdot 1{.}771561\approx\boxed{177{.}16}.$