In a sinking fund of periodic payment ₹R payable at the end of each payment period for n periods, interest being r% per period or $i=\frac{r}{100}$, the amount A that can be discharged is

$R\left[\frac{(1+i)^n-1}{i}\right]$

$\text{Periodic payment}=R.$

$\text{Interest per period } i=\frac{r}{100}.$

$\text{Number of periods}=n.$

$\text{Amount of sinking fund after } n \text{ periods is}$

$A=R\left[\frac{(1+i)^n-1}{i}\right].$

$A=R\frac{(1+i)^n-1}{i}.$