What represents the variance in compound interest on Rs. 5000 over 1 1/2 years at a 4% annual rate when compounded annually versus semi-annually?
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Answer: A. Rs. 2.04
Explanation
Compound interest calculated annually applies the four percent rate once per year over the one and a half year period. Compounding semi annually applies a two percent rate three times across the three distinct six month intervals. Finding the difference between the final compound amounts calculated under both methods yields a variance of two point zero four rupees. Compounding frequency determines how often accumulated interest is added to the principal balance to earn further interest. Semi annual compounding yields slightly higher returns than annual compounding due to more frequent interest accumulation intervals. Compound interest formulas use fractional exponent terms to account for partial years in investment calculations.
Rs. 3.06 overestimates the variance between annual and semi annual compounding calculations through a rounding error. Rs. 4.80 is significantly higher than the actual mathematical difference derived from the compound formulas. Rs. 8.30 represents an incorrect computation that fails to match the precise interest difference.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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