The compound interest on a certain sum for 1 year at 8% p.a., interest compounded half - yearly is Rs. 652.80. What will be the simple interest on the

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The compound interest on a certain sum for 1 year at 8% p.a., interest compounded half - yearly is Rs. 652.80. What will be the simple interest on the same sum for $2 \frac{1}{2}$ years at the same rate of interest ?
1. Rs. 1,680
2. Rs. 1,720
3. Rs. 1,740
4. Rs. 1,600

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Correct Answer - Option 4 : Rs. 1,600

Given:

Compound interest on a certain sum is 652.80

Concept:

Compound interest = P × {(1 + R/100)T - 1} Where, P = Principle, T = Time, R = Rate

Calculation:

Let be assume the principle is P and the rate for half-yearly = 8/2 = 4% T = 2

⇒ P × {(1 + 4/100)2 - 1} = 652.80

⇒ P = 8000

⇒ Simple interest = (8000 × 4 × 5)/100 = 1600

∴ The required result will be 1600.