Increase and Decrease in Compound Percentage

A percentage increase multiplies by $(1 + r)$, and a decrease multiplies by $(1 - r)$, where $r$ is the rate as a decimal.
When the change repeats, you multiply that factor once for each period.
Growing $2\%$ each quarter for a year means multiplying by $1.02$ four times, or $(1.02)^4$.

The key idea is that each change acts on the new amount, not the original.
So two percentage changes in a row do not simply add up.
A $40\%$ markup followed by a $20\%$ discount is $1.40 \times 0.80 = 1.12$, a net $12\%$ increase — not $20\%$.

When interest is compounded several times a year, divide the annual rate by the number of periods.
An $8\%$ annual rate compounded quarterly is $2\%$ per quarter, so after one year the factor is $(1.02)^4$.
Over five years there are $20$ quarters, giving $(1.02)^{20}$.

The same works for repeated decreases.
A $300$ mg dose that loses $15\%$ each hour keeps $85\%$ each hour, so after two hours it is $300 \times (0.85)^2$.
Each hour multiplies by $0.85$ again.

A population of $25000$ grows $2\%$ per year. What is it after $2$ years?
Each year multiplies by $1.02$, so after two years it is $25000 \times (1.02)^2$.
That equals $25000 \times 1.0404 = 26010$.

A shirt priced at $x$ is marked up $40\%$ and then discounted $20\%$. What is the final price?
Markup: $1.40x$. Discount on that: $1.40x \times 0.80$.
So the final price is $1.12x$, a net $12\%$ increase.

A $300$ mg dose decreases $15\%$ each hour. How much is left after $2$ hours?
Each hour keeps $85\%$, so it is $300 \times 0.85 \times 0.85 = 300 \times (0.85)^2$.
That equals $300 \times 0.7225 = 216.75$ mg.