Parveen invested a sum of money at compound interest. It amounted to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the sum and the rate percent per annum.

Rs.2500 and 5%

Rs.2000 and 10%

Rs.2250 and 15%

Rs.100 and 12%

Let's break it down step by step:

The amount after 2 years (A2) = Rs. 2420
The amount after 3 years (A3) = Rs. 2662
The interest earned in the 3rd year (I) = A3 - A2 = Rs. 2662 - Rs. 2420 = Rs. 242
The principal amount (P) = A2 / (1 + r/100)^2, where r is the rate of interest
Substitute A2 and P in the formula: 2420 = P(1 + r/100)^2
Simplify the equation: P = 2000
Now, use the formula: A3 = P(1 + r/100)^3
Substitute A3 and P: 2662 = 2000(1 + r/100)^3
Simplify the equation: r = 10

Answer: Rs. 2000 and 10%