What sum invested at 4% per annum compounded semi-annually amounts to ₹7803 at the end of one year?

Let principal = P.

Given, A = ₹7803.

Since interest is compounded semi-annually,

rate = $\dfrac{4}{2}$% = 2%.

n (the number of conversion periods) = 2.

We know,

A = $P\Big(1 + \dfrac{r}{100}\Big)^n$

Putting values in formula we get,

$7803 = P\Big(1 + \dfrac{2}{100}\Big)^2 \\[1em] 7803 = P\Big(\dfrac{102}{100}\Big)^2 \\[1em] 7803 = P\Big(\dfrac{51}{50}\Big)^2 \\[1em] 7803 = P \times \dfrac{2601}{2500} \\[1em] P = \dfrac{7803 \times 2500}{2601} \\[1em] P = ₹7500.$

Hence, ₹7500 will amount to ₹7803 in 1 year at 4% per annum compounded semi-annually.