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The difference between compound interest and simple interest on a sum for 2 year at 20% per annum is Rs. 200. If the interest is compounded half yearly, then what is the difference (in Rs) between compound and simple interest for 1st year?1). 502). 753). 1004). 150 |
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Answer» Given, ⇒ CI – SI = Rs. 200 Let the principal be P So, we have ⇒ P(1 + R/100n)nt – P - (P × R × T)/100 = 200 ⇒ P(1 + 20/100)2 – P - (P × 20 × 2)/100 = 200 ⇒ 1.44P – P – 0.4P = 200 ⇒ 0.04P = 200 ⇒ P = 200/0.04 = Rs. 5000 Now, the DIFFERENCE when compounded HALF yearly ⇒ [5000(1 + 20/200)2 – 5000] – (5000 × 20 × 1)/100 ⇒ [5000(1.1)2 – 5000] – 1000 ⇒ [5000(1.21) – 5000] – 1000 ⇒ 6050 – 6000 = Rs. 50 ∴ the correct option is 1) |
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