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Depreciation

When an object loses the same percentage of its value every year, the model is exponential with a growth factor less than 1. You do not multiply by the percentage, but by what remains. If a car loses 15% per year, the factor is $0.85$ , and the value after $x$ years is the initial value times $0.85^x$ . The factor should be positive. A negative factor would change sign every year.

V(x) = a\cdot b^x

value after x years

b = 1 - \frac{p}{100}

factor for a loss of p percent

Symbols

$V$	the value	kr
$a$	price when new	kr
$x$	age	years

Example

A car costing 400 000 kr loses 15% per year, so $b = 1 - 0.15 = 0.85$ . After 4 years: $400\,000\cdot 0.85^4 \approx 208\,800$ kr.

A 15% loss of value means that 85% of the value remains, not that you subtract 15.

Practise exponential models for free →

← Compound interest · Percent and percentage points →

Part of Mathematics 1T: Exponential models.