Question
The difference between compound interest and simple interest on a sum for 2 years at 10% per annum , when the interest is compounded annually is Rs. 16. If the interest were compounded half -yearly the difference in two interests would be :
Answer: Option A
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For first year, S.I. = C.I.
Now, Rs. 16 is the S.I. on S.I. for 1 year.
Rs. 10 id S.I. on Rs. 100.
`:.` Rs. 16 is S.I. on Rs.` (100/10 xx 16)` = Rs. 160
So, S,I, on principal for 1 year at 10% is Rs. 160
`:.` principal = Rs. `((100 xx 160)/(10 xx 1))` = Rs. 1600
Amount for 2 years compounded half yearly = Rs. `[1600 xx (1 + 5/100)^4]` = Rs. 1944.81
`:.` C.I. = Rs. (1944.81 - 1600) = Rs. 344.81
S.I. = Rs. `((1600 xx 10 xx 2)/(100))` = Rs. 320.
`:.` (C.I.) - (S.I.) = Rs. (344.81 - 320) = Rs. 24.81.
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