Corporate Accounting and Financial Management · Time Value of Money

Sinking Fund, Capital Recovery and Loan Amortisation Explained

Updated 11 October 2026 · Fact-checked

A sinking fund is a fixed deposit made each period so that it grows to a target sum. Capital recovery is the fixed instalment that repays a loan with interest. Use the annuity formulas: deposit = target ÷ FVIFA, instalment = loan ÷ PVIFA. An amortisation schedule splits each instalment into interest and principal.

Understand Sinking Fund, Capital Recovery and Loan Amortisation

Both problems are annuity problems run in opposite directions. In one you know the future sum and want the regular deposit. In the other you know the present loan and want the regular payment.

A sinking fund is built by equal deposits at the end of each period, earning compound interest. The aim is to reach a target sum on a future date, for example to redeem a debenture or replace a machine. The deposit is found by dividing the target by the future value annuity factor. The sinking fund factor is the reciprocal of that factor.

Capital recovery means repaying a loan through equal periodic payments that cover both interest and principal. The instalment is the loan divided by the present value annuity factor. The capital recovery factor is the reciprocal of the present value annuity factor. It is the EMI per ₹1 borrowed.

A loan amortisation schedule shows each instalment broken into interest and principal. Interest for a period is charged on the opening balance. The rest of the instalment reduces the balance. Because the balance falls, interest falls and the principal part rises, while the instalment stays the same. The closing balance after the last instalment is nil.

Key rules to remember

Future value annuity factor: FVIFA = [(1 + r)ⁿ − 1] ÷ r; r is the rate per period and n the number of periods. Payments are at the end of each period (ordinary annuity).
Sinking fund deposit: A = FV × r ÷ [(1 + r)ⁿ − 1] = FV ÷ FVIFA; The term r ÷ [(1 + r)ⁿ − 1] is the sinking fund factor.
Present value annuity factor: PVIFA = [1 − (1 + r)⁻ⁿ] ÷ r; Use it to value a series of equal end-of-period payments.
Loan instalment (EMI): A = P ÷ PVIFA = P × r ÷ [1 − (1 + r)⁻ⁿ]; The term r ÷ [1 − (1 + r)⁻ⁿ] is the capital recovery factor.
Amortisation schedule rows: Interest = Opening balance × r; Principal = Instalment − Interest; Closing balance = Opening balance − Principal; The closing balance of one period is the opening balance of the next.
Relation of the two factors: Capital recovery factor = Sinking fund factor + r; Useful as a cross-check when both tables are given.

How to solve Sinking Fund, Capital Recovery and Loan Amortisation questions

Decide first whether the question gives a future sum or a present loan. Then follow the same path each time.

1Read the question and mark what is known: target sum or loan amount, rate, number of years, and whether payments are yearly or more often.
2Convert rate and periods to match the payment frequency. For monthly payments, use annual rate ÷ 12 and years × 12.
3Choose the formula. Target sum to deposit: sinking fund. Loan to instalment: capital recovery.
4Find the factor from the table given, or compute (1 + r)ⁿ carefully and then the factor.
5Divide the target by FVIFA, or the loan by PVIFA, to get the payment.
6If a schedule is asked, build columns: year, opening balance, instalment, interest, principal, closing balance.
7Check that the final closing balance is nil (or the sinking fund equals the target). Allow small rounding differences.
8State the answer in rupees with a clear conclusion line.

Quickest way: Use the table factor and the reciprocal

When to use it: Use it when the question supplies PVIFA or FVIFA values, which is common in CS Executive papers.

Pick the factor for the given rate and period from the table.
Divide: deposit = target ÷ FVIFA; instalment = loan ÷ PVIFA.
For a schedule, only compute interest on the opening balance each year. Take principal as instalment minus interest.
In the last year, compute interest first, then check that principal equals the opening balance. Adjust the final instalment slightly for rounding if needed.

Common mistakes in Sinking Fund, Capital Recovery and Loan Amortisation

Using PVIFA for a sinking fund problem, or FVIFA for a loan problem.
Both are annuity factors and the names look alike.
Fix: Ask: is the known amount in the future (use FVIFA) or today (use PVIFA)?
Multiplying by the factor instead of dividing.
Students remember 'multiply by the factor' from simple annuity value problems.
Fix: When the payment is the unknown, divide the lump sum by the factor.
Charging interest on the original loan every year in the schedule.
It is confused with simple interest.
Fix: Charge interest only on the opening balance of that period.
Not adjusting rate and periods for monthly or half-yearly payments.
Students copy the annual rate straight into the formula.
Fix: Divide the rate and multiply the years by the number of payments in a year.
Treating the whole instalment as a reduction in the loan.
The interest part is ignored.
Fix: Split each instalment: interest first, the balance is principal.

Worked examples

Example 1

A company wants a sum of ₹10,00,000 at the end of 4 years to replace a machine. It deposits an equal amount at the end of each year at 10% p.a. compound interest. Find the annual deposit.

Show the solution

Rate r = 10% = 0.10 and n = 4.
(1.10)⁴ = 1.4641.
FVIFA = (1.4641 − 1) ÷ 0.10 = 4.641.
Deposit = 10,00,000 ÷ 4.641 = ₹2,15,471 (approx.).
Check: 2,15,471 × 4.641 ≈ ₹10,00,000.

Answer: The company must deposit about ₹2,15,471 at the end of each year.

Example 2

A loan of ₹1,00,000 is repaid in 3 equal year-end instalments at 10% p.a. on the reducing balance. Find the instalment and prepare the amortisation schedule.

Show the solution

(1.10)³ = 1.331, so (1.10)⁻³ = 0.7513.
PVIFA = (1 − 0.7513) ÷ 0.10 = 2.487.
Instalment = 1,00,000 ÷ 2.487 = ₹40,211 (approx.).
Year 1: interest = 1,00,000 × 10% = ₹10,000; principal = 40,211 − 10,000 = ₹30,211; closing balance = ₹69,789.
Year 2: interest = ₹6,979; principal = 40,211 − 6,979 = ₹33,232; closing balance = ₹36,557.
Year 3: interest = ₹3,656; principal = 40,211 − 3,656 = ₹36,555; closing balance ≈ ₹2, which is a rounding difference and treated as nil.

Answer: The annual instalment is about ₹40,211. Interest falls from ₹10,000 to ₹6,979 to ₹3,656, while the principal repaid rises from ₹30,211 to ₹33,232 to ₹36,555, and the loan is cleared at the end of year 3.

Exam tips

Always write the formula first. Marks are given for method even if the arithmetic slips.
Show the schedule in columns and check the closing balance is nil. It shows the examiner your answer is right.
Read whether payments are at the end or the start of the period. This text assumes end unless stated otherwise.
Work to the rounding the question allows and keep factors to at least three decimals to limit error.
Link the topic to debenture redemption, where a sinking fund is built to repay debentures.

Practice questions from Time Value of Money

Sinking Fund, Capital Recovery and Loan Amortisation: frequently asked questions

What is the sinking fund factor?

It is the equal deposit per period that grows to ₹1 at the end of n periods. It equals r ÷ [(1 + r)ⁿ − 1], the reciprocal of FVIFA. Multiply it by the target sum to get the deposit.

What is the capital recovery factor?

It is the equal payment per period that repays ₹1 of loan over n periods at rate r. It equals r ÷ [1 − (1 + r)⁻ⁿ], the reciprocal of PVIFA. Multiply it by the loan amount to get the instalment.

How does an amortisation schedule change over time?

The instalment stays the same. Interest is highest in the first period because the balance is highest, and then falls. The principal part therefore rises each period until the balance reaches nil.

How do I handle monthly EMIs?

Divide the annual rate by 12 and multiply the years by 12. Then apply the same capital recovery formula using these monthly values.