The difference between annual compound and simple interest on a principal for 2 years at 4% per annum is Re. 1. Find the sum in Rs._________?
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Answer: A. 625
Explanation
The difference between annual compound and simple interest for two years equals principal times the square of the rate percentage. Substituting one for the difference and four percent for the rate gives one equals P times four over one hundred squared. Simplifying the fraction four over one hundred to one over twenty-five squared gives one over six twenty-five, making P equal to six hundred twenty-five. For a two-year period, the difference between compound and simple interest depends solely on the principal and the squared interest rate. Squaring four percent yields sixteen over ten thousand, which simplifies to one over six hundred twenty-five. Solving for the principal involves multiplying the difference by the reciprocal of the squared interest fraction.
Option B results in a fractional interest difference that fails to equal exactly one. Option C produces an interest variance slightly lower than the required one-rupee target. Option D overestimates the principal amount when tested against the four percent two-year difference formula.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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