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If I can assume a value of $100,000 will reduce by a sum of say 25% each year, how do I calculate the amount it will reduce by each month over a period of 3 years.

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2 Answers 2

Suppose that on a monthly basis the amount reduces by a factor of $x$.

We know that we start with $A$ amount then at the end of 1 year the amount reduces to $A/1.25$. (Note: You can interpret 25% reduction in one year as follows as well: $0.75 A$. Even under this interpretation the general idea I show below will work.)

In order to compute $x$ note the following:

  Month     Value
    0       A
    1      A/x
    2      A/x^2
    .       .  
    .       .
   12      A/x^12

Thus, we have that:

$$\frac{A}{x^{12}} = \frac{A}{1.25}$$

Thus, it follows that:

$$x = (1.25)^{(1/12)}$$

At the end of three years it would have reduced by a factor of:

$$x^{36} = (1.25)^{(36/12)}$$

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If you reduce by a factor $1.25$ in a year, you reduce by a factor $1.25^{(\frac{1}{12})}\approx 1.01877$ each month. At the end of $3$ years, it will have reduced by a factor of about $1.953$, or lost almost half its value.

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