The difference between simple interestand compound interest on a sum for 2 years at 8% per annum is Rs.160.If the interests were compounded half-yearly, the difference in interests in two years will be nearly
A
Rs. 5012.2
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B
Rs. 6122.4
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C
Rs. 2468.2
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D
Rs. 4867.2
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Solution
The correct option is ARs. 5012.2 Given, principle amount is same for both simple and compound interest at 8% for 2 years. According to question, C.I.−S.I.=160 ⇒P(1+8100)2−P−P×8×2100=160 ⇒P[(108100)2−1−16100]=160 ⇒P×0.0064=160 ⇒P=25000 If the compound interest was compounded half-yearly, then the new difference between the two interests will be 25000(1+8100)4−25000−25000×8×2100 ⇒34012.22−25000−4000=Rs.5012.22