A sinking fund is money set aside at regular intervals so that, with compound interest, it grows to a known amount needed on a future date — for example to replace an asset or redeem a debt. It is a direct application of the future value of an annuity.

How it works

If you deposit a fixed sum $P$ at the end of each period, those deposits compound into an accumulated value given by the annuity factor. To find the instalment required to hit a target $A$, simply rearrange that relationship.

The target must be the future cost (the replacement price prevailing at the end of the term), never the present cost.

Steps

1. Fix the target future amount $A$ (the replacement cost at term-end).
2. Identify the rate per period $i$ and the number of deposits $n$.
3. Substitute into $P=A\cdot\dfrac{i}{(1+i)^n-1}$ to get each instalment.

Quick example

A firm needs ₹33,100 in 3 years to replace a machine. Deposits earn 10% p.a. What annual deposit is required?

1. $A=33100$, $i=0.10$, $n=3$. …