Sinking Fund

A sinking fund is a pool of money built up through regular, scheduled deposits so that a known amount is available on a known future date. The purpose is fixed in advance — retiring a bond issue at maturity, replacing a roof or a fleet vehicle, funding a lease buy-out — and each deposit is sized so the fund reaches exactly that target.

The term comes from corporate finance, where a bond indenture may require the issuer to "sink" part of the debt over the life of the bond rather than face the whole principal at maturity. The same arithmetic appears in accounting for asset replacement and in budgeting for large, predictable, non-monthly expenses.

How it differs from an amortised loan. An amortising loan starts at the full amount and is paid down to zero; a sinking fund starts at zero and is built up to the full amount. Both run on the same annuity mathematics, in opposite directions.

The formula. A sinking fund is the future value of an ordinary annuity: $n$ level deposits of $PMT$, each made at the end of a period, each earning interest at rate $i$ per period. The accumulated value is

$FV = PMT \cdot \frac{(1+i)^n - 1}{i}.$

Solving for the deposit gives the sinking fund payment:

$PMT = FV \cdot \frac{i}{(1+i)^n - 1}.$

The multiplier $\dfrac{i}{(1+i)^n - 1}$ is known as the sinking fund factor. The rate and the count must refer to the same period: for monthly deposits at a nominal annual rate $r$ compounded monthly, $i = r/12$ and $n$ is the number of months.

Worked example. Suppose an agreement requires $50,000 to be on hand in $5$ years, with deposits made at the end of each month into an account whose contractual rate is $6\%$ nominal, compounded monthly. Then $i = 0.06/12 = 0.005$ and $n = 5 \times 12 = 60$, and

$(1.005)^{60} \approx 1.348850,$

so

$PMT = 50000 \cdot \frac{0.005}{1.348850 - 1} = \frac{250}{0.348850} \approx 716.64.$

A deposit of about $716.64 per month reaches the target. The deposits themselves total 60 \times 716.64 = \42{,}998.40$; the remaining$\approx $7{,}001.60$ is accumulated interest.

Reading the schedule. A sinking fund schedule lists, period by period, the deposit, the interest credited on the existing balance, and the closing balance. Early deposits contribute more interest because they compound for longer, which is why the balance curve is convex rather than a straight line. Setting $i = 0$ collapses the formula to $PMT = FV / n$ — the no-interest case, where each deposit is simply an equal share of the target.

This entry describes the arithmetic only; the rate, term and target in any real agreement come from that agreement's own terms.