A sum amounts to Rs. 1210 in 2 years when invested at compound interest. If principal is Rs. 1000, then what is the rate of interest (in %)?

C = P[(1 + r/100)n - 1]

S = P + C

Where

C = compound interest

P = Principal

r = rate

n = number of period

S = sum after n periods

In 2 years,

P = 1000

S = 1210

⇒ P + C = 1210

⇒ 1000 + C = 1210

⇒ P[(1 + r/100)n - 1] = 210

⇒ 1000 × [(1 + r/100)2 – 1] = 210

⇒ (1 + r/100)2 - 1= 0.210

⇒ (1 + r/100)2 = 1.21

⇒ r/100 = (1.21)1/2 - 1 = 1.1 - 1 = 0.1

⇒ r = 10%