Question

A certain sum of money amounts to Rs. 2420 In two years and Rs. 2662 in three years at some rate of Compound interest, compounded annually. Find the sum and the rate of interest per annum.
1. Rs. 1000 and 12%
2. Rs. 2500 and 5%
3. Rs. 2250 and 15%
4. Rs. 2000 and 10%

Answer 1

Correct Answer - Option 4 : Rs. 2000 and 10%

As we know,

A = P (1 + r/100)^t

2420 = P (1 + r/100)²      ----(i)

Again,

2662 = P (1 + r/100)³      ----(ii)

Divide equation (ii) from equation (i)

2662/2420 = (1 + r/100)

⇒ 2662/2420 - 1 = r/100

⇒ 242/2420 = r/100

⇒ r = 1/10 × 100

⇒ r = 10%

From equation (i)

2420 = P (1 + 10/100)²

⇒ 2420 = P × 11/10 × 11/10

⇒ P = 2420 × 100/121

⇒ P = 2000

∴ P = Rs. 2000 and r = 10%