What sum will amount to ₹28090 in two years at 6% per annum compound interest? Also find the compound interest.

Let principal be ₹P.

We know,

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

Putting values in formula we get,

$\Rightarrow 28090 = P\Big(1 + \dfrac{6}{100}\Big)^2 \\[1em] \Rightarrow 28090 = P\Big(\dfrac{106}{100}\Big)^2 \\[1em] \Rightarrow 28090 = P\Big(\dfrac{53}{50}\Big)^2 \\[1em] \Rightarrow 28090 = P \times \dfrac{53}{50} \times \dfrac{53}{50} \\[1em] \Rightarrow P = \dfrac{28090 \times 50 \times 50}{53 \times 53} \\[1em] \Rightarrow P = \dfrac{28090 \times 2500}{2809} \\[1em] \Rightarrow P = ₹25000.$

C.I. = Final amount - Principal = ₹28090 - ₹25000 = ₹3090.

Hence, the principal = ₹25000 and compound interest = ₹3090.