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.
Calculating monthly reduction in value
2 Answers
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:
$x^{36} = (1.25)^{(36/12)}$
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.