Sinking Fund Calculator
Work out the fixed periodic deposit needed to accumulate a target amount after a number of periods.
Input Data
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At a glance:A sinking fund is an annuity arrangement that, given a target amount to accumulate after a number of periods, works backwards to the fixed periodic deposit needed: PMT = FV × r ÷ ((1+r)^n − 1), where r is the periodic rate (annual rate ÷ deposits per year) and n is total periods (term × deposits per year). It is used by businesses to set aside money to redeem bonds or replace equipment, and by individuals to save regularly for a car, renovation or other large expense — the discipline of pre-funding a known future cost.
Formula
Periodic deposit PMT = FV × r ÷ ((1+r)^n − 1), r periodic rate, n total periods.
Periodic rate r = annual rate ÷ deposits per year; total periods n = term × deposits per year.
Total principal deposited = PMT × n; accumulated interest = target − total principal.
$$\text{PMT} = \dfrac{FV \times r}{(1+r)^n - 1}$$$$r = \dfrac{\text{Annual Rate}}{f}, \quad n = f \times \text{Years}$$How to Use
- Enter the target amount to accumulate after n periods.
- Enter the annual rate, term and deposits per year.
- The periodic deposit, total principal and accumulated interest show instantly.
FAQ
How does a sinking fund differ from a savings plan?
A sinking fund works backwards: set the target amount first, then compute the periodic deposit needed. A savings plan usually sets the deposit first and shows the final accumulation. The two formulas are inverse of each other.
Why is the sum of deposits less than the target?
Because each deposit earns interest in later periods, and that interest fills the gap. Total principal deposited plus accumulated interest equals the target amount.
What if the rate is zero?
With no interest to help, the periodic deposit is simply the target spread evenly across periods: FV ÷ n.
Beyond corporate debt repayment, how can individuals use a sinking fund?
The name sounds corporate, but the underlying wisdom — pre-funding a known future large cost with disciplined instalments — is extremely useful for personal finance. For companies: after issuing bonds, they set aside a fund during the life to redeem the principal at maturity, avoiding a cash crunch. The same logic applies to individuals as 'target savings': rather than scrambling when a big expense hits, identify foreseeable large costs now and deposit a fixed amount monthly. Common personal uses: (1) car replacement — reverse the monthly deposit for a 5-year horizon; (2) home renovation/repairs; (3) children's education; (4) annual large expenses like insurance premiums or tax, split monthly; (5) travel, weddings, big appliance replacement. Benefits: avoids debt (no borrowing or instalments), eases cash-flow pressure (spreads a lump into affordable bits), and lets interest help. This calculator turns a distant goal into a concrete monthly action. Pair with the Savings Plan calculator.
Why is the total deposited less than the target, and is monthly or annual deposit better?
Both relate to how compounding works. First, why total deposit < target: because interest fills the gap. Each deposit earns interest over later periods; the earlier the deposit, the longer it compounds. So final fund = your principal + interest earned; since interest contributes part, the principal you must put in is less than the target. In the example: HK$100,000 in 5 years at 5% monthly gives HK$1,470.46/month, total principal HK$88,227.40, with HK$11,772.60 from interest — you deposit nearly HK$11.8k less. That is the power of compounding early. Second, monthly vs annual: generally higher frequency is better — more compounding events and a more affordable, discipline-friendly monthly rhythm matching most people's income. In the example, monthly principal (88,227) is slightly lower than annual (90,487). But match frequency to reality (annual bonus income, annually-compounding products). The principle: higher frequency + start early maximises compounding, but consistency matters most. Pair with the Savings Plan and Compound Interest calculators.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.