A man borrowed money for $2$ years and paid back in two equal annual instalments of ₹$2,260$ at $5\%$ compound interest, compounded annually. What was the sum (in ₹, to the nearest tens) borrowed?

Given:
* Annual instalment ($I$) = ₹$2,260$
* Rate of interest ($R$) = $5\%$ per annum

The formula for the present value (sum borrowed, $P$) of $2$ equal annual instalments under compound interest is:
$$P=\frac{I}{\left(1+\frac{R}{100}\right)}+\frac{I}{{\left(1+\frac{R}{100}\right)}^2}$$

Here, $\left(1+\frac{5}{100}\right)=1.05=\frac{21}{20}$.
So, the equation becomes:
$$P=\frac{2260}{\frac{21}{20}}+\frac{2260}{{\left(\frac{21}{20}\right)}^2}$$
$$P=2260\times \frac{20}{21}+2260\times \frac{400}{441}$$
$$P=\frac{2260\times 420}{441}+\frac{2260\times 400}{441}$$
$$P=\frac{2260\times (420+400)}{441}=\frac{2260\times 820}{441}$$
$$P=\frac{1853200}{441}\approx 4202.26$$

Rounding to the nearest tens gives ₹$4,200$.