Question

A sum of Rs. 7500 amounts to Rs. 8748 after 2 years at a certain compound interest rate per annum. What will be the simple interest on the same sum for \(2\frac{1}{5}\) years at 2.5 times the earlier interest rate?
1. Rs. 4140
2. Rs. 3300
3. Rs. 2760
4. Rs. 5520

Answer 1

Correct Answer - Option 2 : Rs. 3300

Given:

Principal = Rs. 7500

Amount = Rs. 8748

Time = 2 years

Concept used:

A = P × (1 + r/100)^t

S.I = (P × R × T)/100

where A = amount, P = principal, R = rate of interest and t = time

Calculation:

7500 × (1 + r/100)² = 8748

⇒ (1 + r/100)² = 8748/7500 = 2916/2500

⇒ (1 + r/100)² = (54/50)²

⇒ 1 + r/100 = 54/50

⇒ r/100 = (54/50) - 1 = 4/50

⇒ r = 8%

now,

according to the question,

P = Rs. 7500, r = 8 × 2.5 = 20% and time = 11/5 years

S.I = (7500 × 20 × 11/5)/100

⇒ (7500 × 4 × 11)/100 = 75 × 4 × 11

⇒ 300 × 11 = 3300

∴ The interest is Rs. 3300.