The compound interest earned by Sunil on a certain sum at the end of two years at the rate of 16% p.a., when interest is compounded annually, was ₹864. What was the sum invested by Sunil ?

₹2,500

From the formula for compound interest, we know,

C.I = P(1+$\frac{R}{100})^t$– P

864 = P(1+$\frac{16}{100})^2$– P

864 = P [ (\(\frac{116}{100}\))² - 1 ]

864 = P [ \(\frac{29}{25}\)  × \(\frac{29}{25}\) - 1 ]

864 = P [ \(\frac{841}{625}\)   - 1 ]

864 = P [ \(\frac{216}{625}\)  ]

P = 2500

So, Initial sum is Rs. 2500