Find Percentage to Reduce Cost to Zero over 24 Months I have a starting figure of 100.  My end goal is to reduce this figure by 1/24 its original value over 24 months, so that the end result is 0.
During the first month, I reduce the starting figure by 4.1667% to result in 95.83.
Going forward, I no longer have access to the starting figure.  How can I calculate the percentages needed to evenly reduce the starting figure to zero.
Thanks!!
 A: You reduce by $$\left(4.1666...\times\frac{100}{x}\right)\%$$ at each stage, where $x$ is the amount you have at that stage. If you do this, you reduce the amount by $$\left(4.1666...\times\frac{100}{x}\right)\%\times x=4.1666...$$ which is what you wanted to do.

So at the start, $x=100$, so you reduced by $4.1666...\%$ to obtain $95.8333...$. Next, reduce this value by $\left(4.1666...\times\frac{100}{95.8333...}\right)\%=4.3478...\%$, to obtain $91.666...$, as required. And so on.
A: You require the value to decrease in an arithmetic progression from $1$ to zero over the space of $24$ months.
\begin{eqnarray*}
1, \frac{23}{24}, \frac{22}{24}, \frac{21}{24}, \cdots, \frac{2}{24}, \frac{1}{24},0.
\end{eqnarray*}
So it decrease by $ 100 \times \frac{1}{24}= 4.166 \cdots \% $ in the first month.
It decreses by $ 100 \times \frac{1}{23}= 4.347 \cdots \% $ in the second month.
It decreses by $ 100 \times \frac{1}{22}= 4.545 \cdots \% $ in the third month.
...
It decreses by $ 100 \times \frac{1}{2}= 50 \cdots \% $ in the penultimate month.
It decreses by $ 100 \times \frac{1}{1}= 100 \cdots \% $ in the last month.
A: At the month $n$ the starting value of $100$ is reduced to:
$$
V_n=100-\frac{100}{24}\cdot n
$$
so the percentage of reduction at this stage is
$$
r\%=\frac{\frac{100}{24}}{100-\frac{100}{24}\cdot n}\cdot 100=\frac{100
}{24-n}
$$
