Sinking Fund Factor (A/F)

A sinking fund is money set aside on a schedule so that a known bill can be paid when it arrives — a roof in fifteen years, a pump rebuild in five, a bond redemption at maturity. The factor (A/F, i, n) says what fraction of the target you must deposit each period for the interest to make up the rest. Worked example: at 6% over five years, 1.06⁵ = 1.338226, so the factor is 0.06 ÷ 0.338226 = 0.177396. To have $50,000 in the account you deposit 50,000 × 0.177396 = $8,869.80 a year — not 10,000, because the earlier deposits earn for years before the fund is needed.

The factor's closest relative is the capital recovery factor (A/P), and the two differ by exactly the interest rate: (A/P) = (A/F) + i. Above, 0.177396 + 0.06 = 0.237396, which is what the annual payment on a loan of the same size and term would be per unit borrowed. The reason is worth seeing — owning an asset outright costs you the interest you forgo plus the sinking fund to replace it, which is precisely how an equivalent annual cost is built. The term comes from eighteenth-century British public finance: Robert Walpole's sinking fund of 1717 and William Pitt's revival of it in 1786 were both schemes to retire the national debt by regular set-asides, and both were eventually raided for other purposes, which is the oldest lesson attached to the idea. The trap here is the same one that governs the whole family: i is the rate per deposit period, and n is the number of deposits, not the number of years.