Compound annual depreciation:
value left after a fixed percentage loss each year

A loss of the same share, not the same amount

Compound depreciation applies a fixed percentage to whatever value remains at the start of each year. Because the base shrinks, the rupee amount lost shrinks too: the first year costs more than the second, and the second more than the third.

This pattern matches how many assets actually behave. A vehicle or a laptop loses a big slice of its value in the first year or two and then declines more gently. It is also the logic behind reducing-balance or written-down-value methods in accounting.

The formula and a three-year example

Raising (1 − rate) to the number of years does the repeated multiplication in one step. For a 10% rate, the yearly multiplier is 0.9, so three years means 0.9 × 0.9 × 0.9 = 0.729.

The factor 0.729 is the quickest sanity check: any asset depreciating at 10% retains about 73% of its price after three years.

Watching the amounts shrink

Note that the value never reaches zero under this method; it only gets smaller. That is one reason accountants often combine it with a scrap value or switch to a straight-line method late in an asset's life.

How long until the asset is worth half its price? Divide ln 0.5 by ln 0.9 to get about 6.6 years. That halving time is handy when you are judging a resale decision.

Compound against straight-line

A straight-line method taking 10% of the original price each year would remove ₹10,000 every year and leave ₹70,000 after three. The compound method leaves ₹72,900. In the early years the compound method takes the same first-year amount, but afterwards it takes less, so the book value stays higher for longer.

• Compound (reducing balance): bigger charge early, smaller later, value never reaches zero.
• Straight line: equal charge each year, reaches the chosen residual value exactly at the end of life.
• Which one is allowed for tax or company accounts depends on local rules and the asset class, so check the rule that applies to you rather than assuming either method.

Estimating the rate from real prices

If you know a purchase price and what a similar asset sells for years later, you can back out an implied yearly rate. Divide the later value by the original price, take it to the power of one over the years, subtract the result from one.

Example: something bought for ₹1,00,000 that sells for ₹72,900 after three years has a ratio of 0.729. The cube root is 0.9, so the implied rate is 10%. The result is only an average; real markets are lumpy, with heavy first-year drops and condition-dependent resale prices.

Using the figure when you buy or sell

The calculation is useful before a purchase as well as for bookkeeping. If you plan to buy equipment for ₹1,00,000 and sell it after three years, the 10% yearly pattern suggests it will still hold about ₹72,900 of value, so the real cost of ownership is closer to ₹27,100 plus running costs than to the full price.

Compare two options by their depreciation, not just their sticker price. A cheaper item that loses 20% a year can cost more over three years than a pricier one that loses 10%. At 20%, ₹80,000 becomes 80000 × 0.8³ = ₹40,960, a loss of ₹39,040, which is more than the ₹27,100 lost on the ₹1,00,000 item.

An expense total tool helps you add purchase price, running cost and servicing before comparing. Then subtract the expected resale value from the depreciation curve to get a net cost of ownership for each option.

Setting it up in a spreadsheet

In a spreadsheet, put the price in one cell, the rate as a decimal in another and the years in a third. The closing value is then price × (1 − rate)^years. To get the yearly charge for any single year, subtract that year's closing value from the previous one rather than applying the rate to the original price.

A common slip is using the rate on the original price each year, which turns the schedule into a straight line by accident. Another is leaving the rate as 10 rather than 0.10, which produces a negative base. If the closing value is a tiny or negative number, the rate has probably been entered as a whole number.

For monthly schedules, convert the annual rate to a monthly multiplier by taking the twelfth root of (1 − annual rate). For 10% a year that multiplier is about 0.99126, a monthly loss of roughly 0.87%, which is slightly less than one-twelfth of 10%.

Where the number misleads

• Use whole years in the formula, or convert months to a fraction of a year carefully; 18 months is an exponent of 1.5.
• Market value and book value are different. The formula gives a book-style estimate, not what a buyer will actually pay.
• Improvements, accidents and unusual mileage or usage make real values diverge from any smooth curve.
• For tax computations, follow the official depreciation rates and conventions in force, which can differ from a simple formula.