# Sum of Year Digits Method

by Philo Gabriel; Updated September 26, 2017Sum of year digits is an accounting technique used to calculate depreciation. The depreciation is accelerated to reflect that items lose value more rapidly early in their history than late -- e.g., your new car suffers its greatest loss of value the day you drive it away from the dealership. The sum of year digits method accelerates depreciation more rapidly than the straight line method, and less rapidly than the declining balance method.

### What You Will Need to Calculate Sum of Year Digits Depreciation

In order to calculate the depreciation for an item of property using the sum of year digits method, you will need to plug into the formula at least the best estimate for each of the following:

Original cost Number of years of anticipated use Expected value at the end of its period of anticipated use

### Calculating Sum of Year Digits Depreciation

First, subtract the value you expect the item to have at the end of its period of anticipated use from its original cost. This is its total depreciable cost.

Next, take the sum of the digits up to and including the number of years of anticipated use of the item. For one year, this would be one. For two years, this would be 1 + 2, or 3. For three years, this would be 1 + 2 + 3, or 6. For four years, this would be 1 + 2 + 3 + 4, or 10, and so on. A simple way to calculate this is n(n + 1)/2 for n years. For example, for eight years, this would be 8(8 + 1)/2, or (8 * 9)/2, or 72/2, or 36.

Multiply the total depreciable cost by a fraction consisting of the above sum of digits as the denominator, and the number of years of anticipated use as the numerator. This is the depreciation for the first year.

Multiply the total depreciable cost by that same fraction except with a numerator of one less. This is the depreciation for the second year.

To calculate each subsequent year’s depreciation, continue this same procedure, deducting one from the numerator for each year. The numerator should equal one the final year of anticipated use.

### Example #1

You purchase a $4,000 camcorder for your filmmaking business. You anticipate using it for three years and being able to sell it used for about $1,000 after that time.

The camera’s depreciable cost is $3,000 over 3 years. The sum of digits is 1 + 2 + 3 = 6.

Its yearly depreciation is:

Year 1: $3,000 * 3/6 = $1,500 Year 2: $3,000 * 2/6 = $1,000 Year 3: $3,000 * 1/6 = $500

### Example #2

Your company invests in a truck that costs $25,000. You expect to use it for four years, and to sell it for $5,000 after that time.

The truck’s depreciable cost is $20,000 over five years. The sum of digits is 1 + 2 + 3 + 4 + 5 = 15.

Its yearly depreciation is:

Year 1: $20,000 * 5/15 = $6,667 Year 2: $20,000 * 4/15 = $5,333 Year 3: $20,000 * 3/15 = $4,000 Year 4: $20,000 * 2/15 = $2,667 Year 5: $20,000 * 1/15 = $1,333

### Example #3

Your company purchases an assembly line robot for $40,000. It is expected to be usable for seven years, after which it will have no value and will be discarded.

The robot’s depreciable cost is $40,000 over seven years. The sum of digits is 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28, or 7(7 + 1)/2 = 28.

Its yearly depreciation is:

Year 1: $40,000 * 7/28 = $10,000 Year 2: $40,000 * 6/28 = $8,571 Year 3: $40,000 * 5/28 = $7,143 Year 4: $40,000 * 4/28 = $5,714 Year 5: $40,000 * 3/28 = $4,286 Year 6: $40,000 * 2/28 = $2,857 Year 7: $40,000 * 1/28 = $1,429

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