The difference between the simple interest and the compound interest on a sum of money for 2 years at 12% per annum is ₹ 216. Find the sum.

Given,

n = 2 years

r = 12%

Let sum of money be ₹ P.

C.I. = A - P

$C.I. = P\Big(1 + \dfrac{r}{100}\Big)^n - P \\[1em] = P\Big(1 + \dfrac{12}{100}\Big)^2 - P \\[1em] = P \times \Big(\dfrac{112}{100}\Big)^2 - P \\[1em] = P \times \Big(\dfrac{28}{25}\Big)^2 - P\\[1em] = P \times \dfrac{784}{625} - P \\[1em] = \dfrac{784P}{625} - P \\[1em] = \dfrac{784P - 625P}{625} \\[1em] = \dfrac{159P}{625}.$

By formula,

T = 2 years

$S.I. = \dfrac{P \times R \times T}{100} \\[1em] = \dfrac{P \times 12 \times 2}{100} \\[1em] = \dfrac{6P}{25}.$

Given,

Difference between S.I. and C.I. = ₹ 216

$\Rightarrow \dfrac{159P}{625} - \dfrac{6P}{25} = 216 \\[1em] \Rightarrow \dfrac{159P - 150P}{625} = 216 \\[1em] \Rightarrow \dfrac{9P}{625} = 216 \\[1em] \Rightarrow P = \dfrac{216 \times 625}{9} \\[1em] \Rightarrow P = 24 \times 625 \\[1em] \Rightarrow P = ₹ 15,000.$

Hence, sum = ₹ 15,000.