Sinking Funds: Formula, Examples, and Applications

A sinking fund is a savings plan in which equal deposits are made regularly so that they accumulate, with interest, to a target amount on a known future date. It is the mirror image of amortisation: instead of paying down a debt, you build up an asset.

This matters because large future expenses, from replacing factory machinery to redeeming a bond issue, cannot be paid out of a single year's cash flow. A sinking fund spreads the burden into small, predictable deposits and lets compound interest do part of the work.

Key Concepts

• Target amount (S): the sum the fund must reach on the target date. Periodic deposit (R): the equal amount set aside each period.
• Accumulation rate (j): the interest rate the fund earns per deposit period.
• Sinking fund factor: R / S, the deposit needed per unit of target; it falls as the rate rises or the horizon lengthens.
• Sinking fund vs amortisation: amortisation starts with a debt and ends at zero; a sinking fund starts at zero and ends at the target.

Formulas

With deposits R at the end of each period for n periods at rate j per period, the accumulated value is S = R × s-angle-n = R × [(1 + j)^n − 1] / j. Solving for the required deposit: R = S × j / [(1 + j)^n − 1]. If deposits are made at the beginning of each period, multiply the accumulation by (1 + j). These assume a constant earning rate, equal on-time deposits, and no withdrawals.

Worked Example

A company must accumulate ₹10,00,000 in 5 years to replace equipment, and its fund earns 8% per year with annual deposits. The accumulation factor is s-angle-5 = [(1.08)^5 − 1] / 0.08. Since 1.08^5 = 1.46932808, the numerator is 0.46932808 and dividing by 0.08 gives 5.86660101. The required annual deposit is R = 10,00,000 / 5.86660101 = ₹1,70,456.50. Five deposits total 5 × 1,70,456.50 = ₹8,52,282.50; the remaining ₹1,47,717.50 comes from interest earned on the growing fund. If the company waited and saved without interest, it would need ₹2,00,000 per year, so compounding saves nearly ₹30,000 annually.

Common Misconceptions

• A sinking fund is just an emergency fund. An emergency fund covers unknown surprises; a sinking fund targets a known future cost with a calculated deposit schedule.
• It is the same as paying off a loan. Amortisation retires existing debt, while a sinking fund accumulates assets for a future obligation; the formulas are related but the cash flows run in opposite directions.
• You can divide the target by the number of years. That ignores the interest the deposits earn; the correct divisor is the annuity accumulation factor s-angle-n, which is larger than n.

Real-World Applications

Sinking funds retire bond issues at maturity, replace plant and machinery, fund lease balloon payments, accumulate university endowment payouts, and let governments pre-fund pension liabilities.

A sinking fund converts one intimidating future bill into small regular deposits, with compound interest covering part of the target, provided the deposits start early and stay on schedule.