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Accounting · Depreciation and Amortisation

Other Methods of Depreciation (CA Foundation Accounting)

Updated 1 October 2026

Other methods of depreciation spread an asset's cost using rules besides straight line and WDV. Sum of years digits and machine hour rate give a charge each year by fraction or usage. Annuity, depreciation fund and insurance policy methods also deal with interest or replacement funds. Identify the method, compute the yearly charge, then pass entries.

Understand Other Methods of Depreciation

Straight line and WDV are the two main methods. But some assets lose value in other ways, and some businesses want cash ready to replace the asset. The other methods cover these cases.

Sum of years digits (SYD) charges more depreciation in early years and less later. Each year gets a fraction of the depreciable amount. The numerator is the years of life remaining at the start of that year. The denominator is the sum of the digits 1 to n.

Machine hour rate ties depreciation to use. You divide the depreciable amount by the total estimated working hours. Then you multiply by the hours actually worked in the year. Depletion works the same way for mines, quarries and oil wells. The base is the total quantity expected to be extracted, not hours.

Annuity method treats the money invested in the asset as earning interest. Each year the asset account is debited with interest at the given rate on its opening book value. It is then credited with the annuity, which is the depreciation for the year. Profit and Loss is debited with depreciation (the annuity) and credited with interest as income. So the net charge to Profit and Loss is the annuity less the interest. When the annuity is sized correctly, the asset's book value falls to its scrap value by the end of life. Questions usually give the annuity from a table.

Depreciation fund method and insurance policy method are about replacement. The asset stays in the books at original cost. Each year you charge a fixed amount to Profit and Loss and credit it to a Depreciation Fund Account. In the fund method, you invest that amount in outside securities. In the insurance policy method, you pay it as a premium to an insurance company. At the end of life, the investments are sold, or the policy matures, and the cash buys a new asset.

Key rules to remember

Sum of years digits (denominator)
Sum of digits = n(n + 1) ÷ 2
n is the useful life in years. For 4 years the sum is 10 (1 + 2 + 3 + 4).
SYD depreciation for a year
Depreciation = (Cost − Scrap value) × Remaining life at start of year ÷ Sum of digits
Remaining life is n for year 1, n − 1 for year 2, and so on. Total over the life equals Cost − Scrap value.
Machine hour rate
Rate per hour = (Cost − Scrap value) ÷ Total estimated working hours
Yearly depreciation = Rate per hour × Hours worked in that year.
Depletion
Depletion per unit = (Cost − Residual value) ÷ Total estimated quantity; Depletion for year = Per-unit rate × Quantity extracted
Used for mines, quarries and wells. Residual value is often nil if the question says nothing.
Annuity method: yearly asset entries
Interest = Interest rate × Opening book value. Asset A/c Dr (interest), to Interest A/c. Depreciation A/c Dr (annuity), to Asset A/c.
Interest is debited to the asset account and credited to Interest A/c, which is transferred to Profit and Loss as income. The annuity is credited to the asset account and debited as depreciation. Net Profit and Loss charge = Annuity − Interest. When the annuity is sized correctly, book value at end of life equals scrap value.
Depreciation fund: yearly fund credit
Fund credit = Annual contribution + Interest on opening fund investments
Interest received is credited to the fund, not to Profit and Loss. The contribution is charged to Profit and Loss.
Insurance policy method: yearly premium
Depreciation Fund Policy A/c Dr, to Bank A/c (premium paid). Profit and Loss A/c Dr, to Depreciation Fund A/c (same amount). On maturity: Bank A/c Dr, to Depreciation Fund Policy A/c.
After maturity, the balance left in the Depreciation Fund Policy A/c is transferred to the Depreciation Fund A/c. The cash received is then used to replace the asset.

How to solve Other Methods of Depreciation questions

Use this order for any question on these methods. Name the method first, because each one has a different base.

  1. 1Read the question and identify the method. Look for words such as hours, quantity extracted, annuity, fund, policy or sum of digits.
  2. 2Write down the cost, scrap or residual value, life, and any rate given. Compute the depreciable amount (Cost − Scrap) if the method needs it.
  3. 3For SYD, find n(n + 1) ÷ 2, then take the fraction for each year. For machine hour or depletion, find the rate per hour or per unit.
  4. 4Compute the charge for each year asked. Check that all years together equal the depreciable amount.
  5. 5For annuity, work out interest on the opening book value, add it to the asset, and subtract the annuity. For fund and policy methods, work out the contribution or premium and the interest.
  6. 6Pass the journal entries in order: charge to Profit and Loss, investment or premium, interest received, transfer of interest to the fund.
  7. 7Prepare the asset account and, if asked, the fund or policy account. Balance them, showing the closing balance clearly.
  8. 8Check the closing figure: book value at scrap for SYD and annuity, or fund equal to the cost recovered.

Quickest way: Fast working format for these methods

When to use it: Use this when the question asks for depreciation figures for several years and then an account or journal. Time is short and step marks matter.

  1. Draw a small table first with columns Year, Fraction or hours, Depreciation, Book value. Fill it row by row.
  2. Write the formula in one line before using it. This earns method marks even if arithmetic slips.
  3. For SYD, write the fractions in a row (4/10, 3/10, 2/10, 1/10) and check that the numerators add up to the sum of digits.
  4. For fund questions, write each year's fund credit as 'contribution + interest' in one line, and keep a running fund total.
  5. Show journals with narration in one line each. Keep the asset account at cost in fund and policy methods.
  6. Spend the last minute on the check: total depreciation equals cost less scrap, or fund equals the amount needed.

Common mistakes in Other Methods of Depreciation

  • Using full cost instead of Cost − Scrap value in SYD and machine hour methods.

    Students remember the fraction but forget the base differs from WDV.

    Fix: Write 'Depreciable amount = Cost − Scrap' as your first line every time.

  • Taking the wrong numerator in SYD, such as using the year number (1, 2, 3) instead of the remaining life (n, n − 1, ...).

    The year number looks like the natural digit to use.

    Fix: Year 1 gets the biggest fraction. Check that your fractions fall each year and the numerators sum to n(n + 1) ÷ 2.

  • Reducing the asset account in the depreciation fund and insurance policy methods.

    Students carry over the habit from SL and WDV, where depreciation is credited to the asset.

    Fix: In these two methods the asset stays at original cost. The credit goes to the Depreciation Fund Account.

  • Crediting interest on fund investments to Profit and Loss.

    Interest looks like normal income.

    Fix: Transfer the interest to the Depreciation Fund Account. Only the yearly contribution is charged to Profit and Loss.

  • Calculating annuity interest on cost every year instead of on the opening book value.

    Students forget the asset balance changes each year.

    Fix: Use the opening balance of the asset account each year. Interest falls as the balance falls.

  • Applying machine hour rate on estimated hours for the year instead of actual hours worked.

    Both numbers appear in the question.

    Fix: The rate uses total estimated life hours. The charge uses hours actually worked in the year.

Worked examples

Example 1

A machine costing ₹2,60,000 has an estimated scrap value of ₹20,000 and a life of 4 years. Calculate depreciation for each year and the book value at the end of each year under the sum of years digits method.

Show the solution
  1. Depreciable amount = 2,60,000 − 20,000 = ₹2,40,000.
  2. Sum of digits = 4 × 5 ÷ 2 = 10.
  3. Year 1: 2,40,000 × 4 ÷ 10 = ₹96,000. Book value = 2,60,000 − 96,000 = ₹1,64,000.
  4. Year 2: 2,40,000 × 3 ÷ 10 = ₹72,000. Book value = 1,64,000 − 72,000 = ₹92,000.
  5. Year 3: 2,40,000 × 2 ÷ 10 = ₹48,000. Book value = 92,000 − 48,000 = ₹44,000.
  6. Year 4: 2,40,000 × 1 ÷ 10 = ₹24,000. Book value = 44,000 − 24,000 = ₹20,000.
  7. Check: 96,000 + 72,000 + 48,000 + 24,000 = ₹2,40,000. Closing book value equals scrap value.

Answer: Depreciation: Year 1 ₹96,000; Year 2 ₹72,000; Year 3 ₹48,000; Year 4 ₹24,000. Book values: ₹1,64,000; ₹92,000; ₹44,000; ₹20,000.

Example 2

A firm buys machinery for ₹5,00,000 with an estimated scrap value of ₹50,000 and total working life of 90,000 hours. It works 12,000 hours in year 1 and 15,000 hours in year 2. Find depreciation for each year and the book value at the end of year 2 under the machine hour rate method.

Show the solution
  1. Depreciable amount = 5,00,000 − 50,000 = ₹4,50,000.
  2. Rate per hour = 4,50,000 ÷ 90,000 = ₹5.
  3. Year 1 depreciation = 12,000 × 5 = ₹60,000.
  4. Year 2 depreciation = 15,000 × 5 = ₹75,000.
  5. Total depreciation for two years = 60,000 + 75,000 = ₹1,35,000.
  6. Book value at end of year 2 = 5,00,000 − 1,35,000 = ₹3,65,000.

Answer: Rate ₹5 per hour. Depreciation: Year 1 ₹60,000; Year 2 ₹75,000. Book value at end of year 2 is ₹3,65,000.

Example 3

A firm owns machinery costing ₹5,00,000 with a life of 10 years. It uses the depreciation fund method and contributes ₹50,000 at the end of each year, investing it in securities. Interest earned is 10% on the investments held at the start of the year. Pass journal entries for year 1 and year 2, and find the balance of the Depreciation Fund Account at the end of year 2.

Show the solution
  1. End of year 1: Profit and Loss A/c Dr ₹50,000 to Depreciation Fund A/c ₹50,000.
  2. End of year 1: Depreciation Fund Investment A/c Dr ₹50,000 to Bank A/c ₹50,000.
  3. Fund balance at end of year 1 = ₹50,000.
  4. Year 2 interest = 10% of 50,000 = ₹5,000.
  5. Bank A/c Dr ₹5,000 to Interest on Depreciation Fund Investment A/c ₹5,000.
  6. Interest on Depreciation Fund Investment A/c Dr ₹5,000 to Depreciation Fund A/c ₹5,000.
  7. Profit and Loss A/c Dr ₹50,000 to Depreciation Fund A/c ₹50,000.
  8. Depreciation Fund Investment A/c Dr ₹55,000 to Bank A/c ₹55,000. (Interest ₹5,000 plus contribution ₹50,000 is invested.)
  9. Fund balance at end of year 2 = 50,000 + 5,000 + 50,000 = ₹1,05,000.
  10. Investments at end of year 2 = 50,000 + 55,000 = ₹1,05,000, which matches the fund. The machinery stays in the books at its cost of ₹5,00,000.

Answer: Depreciation Fund A/c balance at end of year 2 is ₹1,05,000, matched by investments of ₹1,05,000. The machinery stays at its cost of ₹5,00,000.

Exam tips

  • Read the first line of the question to decide the method. Marks are lost most often by using the wrong base.
  • In fund and policy questions, journal entries are usually the main marks. Practise the sequence: contribution, investment, interest received, interest transferred.
  • For SYD and machine hour, always show the final check that total depreciation equals Cost − Scrap, unless the asset is not fully written off in the period asked.
  • If the annuity is not given, expect it to be stated or taken from a table in the question. Do not try to derive it unless the question asks.
  • Show the asset account or fund account in proper ledger form with dates and balancing figures when asked. Do not skip the carry-forward line.

Practice questions from Depreciation and Amortisation

Other Methods of Depreciation: frequently asked questions

What is the annuity method of depreciation?

It treats the asset purchase as an investment that earns interest. Each year the asset account is debited with interest on its opening book value and credited with the annuity, which is the depreciation. Profit and Loss is debited with the annuity and credited with interest, so the net charge is annuity less interest. The asset reaches scrap value at the end of life.

How is the depreciation fund method different from the insurance policy method?

In both methods the asset stays at cost and a fund is built to replace it. In the fund method, the yearly amount is invested in securities, which earn interest. In the insurance policy method, it is paid as a premium to an insurer, and the policy amount is received at maturity.

How do I calculate sum of years digits depreciation?

Find the sum of the digits from 1 to n using n(n + 1) ÷ 2. Multiply the depreciable amount (Cost − Scrap) by the remaining life at the start of the year, then divide by that sum. Year 1 uses n, year 2 uses n − 1, and so on.

When do I use the machine hour rate method?

Use it when the question gives total estimated working hours and the actual hours worked each year. Depreciation then varies with use. It suits machines where wear depends on how much they run.