Sinking Fund

A sinking fund is a fund built up by setting aside an equal sum at regular intervals so that a known amount is available at a future date — typically to replace a worn-out asset, redeem (pay off) a debenture or bond issue on maturity, or meet any large lump-sum obligation that can be foreseen. The regular deposits earn compound interest, so the fund grows faster than the deposits alone.

A sinking fund is therefore just a future-value annuity read backwards: the target amount $A$ is known, and we need the equal periodic deposit $P$ that will accumulate to it. Rearranging the future-value formula of §2 for $P$:

where $A$ is the amount required at the end, $i$ the rate per period and $n$ the number of deposits. The factor $\\dfrac{i}{(1+i)^n-1}$ is called the sinking-fund factor; it is the exact reciprocal of the future-value annuity factor of §2, which is why a sinking-fund deposit, once found, can always be checked by feeding it back into the ordinary future-value formula and confirming it reproduces the target $A$ (Worked Example 6 does exactly this).

Sinking fund contrasted with loan repayment. Both spread a large sum into equal instalments, but in opposite directions in time:

• A sinking fund accumulates deposits to reach a future amount — it is a future-value problem ($P$ from $A$).
• A loan repayment pays off a sum borrowed today — it is a present-value problem ($P$ from $V$, §6). …