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Find the total compound interest when a sum of Rs. 2000 compounded annually and half-yearly at a rate of interest of 10% for a year.
1. Rs. 300
2. Rs. 400
3. Rs. 380
4. Rs. 405

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Correct Answer - Option 4 : Rs. 405

Formula:

Let  P = Principle, R = rate of interest and N = time period

Compound interest (annually) = P(1 + R/100)N – P

Compound interest (half - yearly) = P{1 + (R/2)/100}2N – P

Calculation:

Here, P = Rs. 2000, R = 10% and N = 1

Compound interest (annually) = 2000(1 + 10/100)1 – 2000 = Rs. 200

Compound interest (half - yearly) = 2000(1 + (10/2)/100)2 – 2000 = Rs. 205

Total compound interest = 200 + 205 = Rs. 405

∴ The total compound interest is Rs. 405.

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