The difference between the simple interest and compound interest (interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is Rs. 4375. What will be the principal?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. Rs. 280000.
| Understanding/Application |
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Let principal be 100x Rate = r = 25% time = t = 1 year Simple interest = Prt/100 = (100x × 25 × 1)/100 = 25x |
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Compound Interest (compounded half yearly for 1 year) = P[(1 + r/200)2 - 1] = 100x[(1 + 25/200)2 - 1] = 100x[(9/8)2 - 1] = 100x × (17/64) = Rs. 26.5625x Difference = 26.5625x - 25x = 4375 x = 4375/1.5625 x = 2800 Principal = 100x = 100(2800) = Rs. 280000 |