Depreciation

Grade 5

What is depreciation?

Depreciation is the fall in value of an asset over time. A new car, a laptop, or a piece of machinery is worth less each year it's used — and that loss of value is depreciation.

The key thing to understand is that depreciation typically works like compound interest in reverse: the drop is calculated as a percentage of the current value each year, not the original price. So the actual amount lost gets smaller every year, even though the percentage stays the same.

The multiplier — below 1 this time

If something loses 15% of its value each year, it keeps 85% of its value. That makes the multiplier 0.85. After n years:

Value after n years = Starting value × multiplier^n

For a depreciation rate of r% per year, the multiplier is (1 − r/100). Losing 20% → multiply by 0.80. Losing 8% → multiply by 0.92. Same logic as compound interest, just smaller than 1.

Worked example

EXAMPLE

A car is bought for £12 000. It depreciates at 18% per year. What is it worth after 4 years?

The multiplier is 1 − 0.18 = 0.82. Raise it to the power 4: 0.82⁴ = 0.45212176. Multiply: 12 000 × 0.45212176 =£5 425.46 (to the nearest penny). The car has lost more than half its value in four years — which is typical for new vehicles.

Don't get caught out

A common mistake is to work out 18% of £12 000 (= £2 160) and then just multiply by 4 to get the total drop. That treats it as simple depreciation and gives £8 640 lost — leaving £3 360 — which is too harsh a drop. The compound method gives £6 574.54 lost, leaving £5 425.46, because each year's depreciation is based on that year's lower value, not the original price. Always use the multiplier method for percentage depreciation questions.

Try this one

An amount \( A \) is increased by \( 20\% \) and then the result is increased by \( 20\% \) again.

Write the overall change as a single percentage increase.

[3]

Nova's hint:

This combines two compound increases into one. Multiply the two multipliers together.

Ask yourself: 'what single multiplier equals applying 1.2 twice?' Compare the combined multiplier with 1.

Try to Solve it with Nova?