Inflation and purchasing power

Statement

Price inflation is $5\%$ per year. In $2024$ a stuffed dumpling costs $2$ euros, so with $40$ euros one can buy $20$ of them. Find the price of the dumpling in $2074$ and how many dumplings can be bought in $2074$ with the same $40$ euros.

Solution

From $2024$ to $2074$ there are $50$ years. The price grows by $5\%$ each year: $p_{2074}=2\cdot 1.05^{50}\approx 2\cdot 11.467\approx 22.93\ \text{euros}.$ With $40$ euros one can buy $\frac{40}{22.93}\approx 1.74\ \to\ 1\ \text{dumpling}$ (only one whole dumpling can be bought).

$\boxed{p_{2074}\approx 22.93\ \text{€};\qquad 1\ \text{dumpling}}$