Depreciation: Understanding Value Decrease

Imagine you've just bought the latest smartphone. A year later, despite it still working perfectly, it's not worth as much as when you purchased it. This decrease in value over time is known as depreciation. Depreciation helps us measure how much value is lost each year

How Does Depreciation Work?

When something depreciates, it loses a certain percentage of its value every year. This is common for things like cars, electronics, or equipment. Just like how interest makes money grow, depreciation does the opposite—it shrinks the value.

The formula for depreciation is very similar to growth and decay:

$$New Value = Original Value \times ( 1 - \frac{Rate}{100} )^t$$

where:

• New Value is the value after depreciation.
• Original Value is the starting value.
• Rate is the percentage of depreciation each year.
• $t$ is the time in years

Tip: For depreciation, you always use a minus sign in the formula since the value is decreasing

 

Example : Understanding Depreciation

Question: You buy a car for $\pounds 15,000$, and it depreciates by $15\%$ each year. What will it be worth after 3 years?

1. Identify the values:

   • Original Value = $\pounds 15,000$
   • Depreciation Rate = $15\%$
   • Time $t = 3$
2. Plug into the depreciation formula: $$New Value = 1500 \times ( 1 - \frac{15}{100} )^3$$
3. Calculate: $$= 1500 \times (0.85)^3$$
4. Solve: $$15000 \times 0.614125 = \pounds 9211.88$$