How Do You Calculate Annual Depreciation?

Annual depreciation is usually calculated by multiplying the asset's value by a fixed annual depreciation rate. For reducing-balance depreciation, multiply the value by $1-r$ each year, where $r$ is the depreciation rate written as a decimal.

This is part of SL 1.4 Financial applications, where depreciation is modelled as a geometric sequence because the value is multiplied by the same factor each year.

If an asset has initial value $V_0$, annual depreciation rate $r$, and value $V_n$ after $n$ years, then

$$V_n=V_0(1-r)^n.$$

The depreciation multiplier is $1-r$. For example, a depreciation rate of $15\%$ gives

$$1-r=1-0.15=0.85.$$

Suppose a car initially costs 20,000 dollars and depreciates by $15\%$ each year. Its value after four years is

$$V_4=20\,000(0.85)^4=10\,440.125.$$

Therefore, the car is worth 10,440.13 dollars after four years, to two decimal places.

The amount lost during a particular year is found from the value at the beginning of that year. During the first year,

$$20\,000(0.15)=3\,000.$$

During the second year, the loss is

$$17\,000(0.15)=2\,550.$$

After four years, the total depreciation is the original value minus the remaining value:

$$20\,000-10\,440.125=9\,559.875.$$

This differs from the depreciation charged during the fourth year. To find that year's loss, first calculate the value after three years and then multiply by the rate:

$$20\,000(0.85)^3(0.15)=1\,842.375.$$

Thus, fourth-year depreciation is 1,842.38 dollars. For a monetary loss, subtract consecutive values or multiply the opening value by $r$.

The depreciation amount decreases each year, although the percentage remains constant.

A common misconception is to subtract the same monetary amount every year. That would be linear depreciation, not percentage reducing-balance depreciation. Unless the question specifies a fixed annual amount, use repeated percentage decrease.

In an IB Math AI exam, show the multiplier and the substituted model before giving the GDC value. Keep full precision until the final answer, round money to two decimal places, and distinguish between the asset's remaining value and the total amount depreciated.