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%
Explanation
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%
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