Discussion
The compound interest on ₹3,90,625 in 2 years at 8% per annum, the interest being compounded half-yearly, is:
Answer: B
The compound interest is Rs 66,351. Compounded half-yearly for 2 years at 8% a year means 4 periods at 4%.
\[ A = 390625 \times \left(\frac{26}{25}\right)^{4} \]\[ A = 456976 \]\[ CI = 456976 - 390625 \]\[ = 66351 \]Rs 456976 is the amount, not the interest. Simple interest would be Rs 62,500, and the other options do not equal the compound interest.
The step of halving the rate and doubling the periods is the key to half-yearly compounding: 8% a year becomes 4% for each of the four half-years. The amount is 390625 × 1.04 four times over, which is Rs 4,56,976, and the compound interest is the amount minus the principal. Rs 66,351 is therefore the interest and Rs 4,56,976 is not.
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