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The difference between compound interest and simple interest on a sum for 2 years at 20% per annum, when the interest is compounded annually is ₹32. If the interest were compounded half-yearly, the difference in two interests would be:

Solution

✅ Correct Option: 3

For two years, difference =P(r100)2=P(0.04)=32= P\left(\frac{r}{100}\right)^2 = P(0.04) = 32, so P=800P = 800.

Half-yearly: rate 10%10\% per half year for 44 periods, so CI =800(1.14−1)=800×0.4641=371.28= 800(1.1^4 - 1) = 800 \times 0.4641 = 371.28.

SI =800×0.20×2=320= 800 \times 0.20 \times 2 = 320.

Difference =371.28−320=₹51.28= 371.28 - 320 = ₹51.28.

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