Suppose you bought a $2500 computer. Changing technology depreciates its value to $972.54 in 3 years.

It depreciated ?% per year (to the nearest percentile)? The answer is 27. I can't see how.

Nice try Tom, but that doesn't really answer why, just how.

We know that the present value of the computer is $972.54. The original value was $2500, and it depreciated yearly over the course of 3 years. Using the compound interest formula as applied to *depreciation*, we can set this up as:

927.54 = 2500 (1 - r )^3 where r = the rate of depreciation. Now divide both sides by 2500 to get

0.389 = (1 - r )^3 now take the cube root of each side to get

0.73 = 1 - r and finally, solving for r, we get

r = 0.27 = 27%

If it depreciates by 27% each year, then that's the same as saying it will retain 73% of its value each year.

After 3 years, its new value will be 73% of 73% of 73% of its initial value.

So after 3 years is will be worth $2500 x (0.73)^3 = $972.5425 exactly, or $972.54 rounded.