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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. 18. If the interest were compounded half-yearly, the difference between the interests would be:
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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. 18. If the interest were compounded half-yearly, the difference between the interests would be:
1). 14
2). 16
3). 28
4). 20
1 answers
4 vote
Let suppose that principal is P
Difference between S.I and C.I is (D) = Rs. 18
The rate of interest (R) = 10%
⇒? $(\frac{R}{{100\;}} = \;\sqrt {\frac{D}{P}} )$
⇒? $(\frac{10}{{100\;}} = \;\sqrt {\frac{18}{P}} )$
P = 1800
Amount compounded half yearly = Rs. [1800 × (1 + 5/100)4] = Rs. 2187.91 = Rs. 2188
⇒ C.I. = Rs. (2188 – 1800) = Rs. 388
⇒ S.I. = Rs. (1800 × 10 × 2)/100 = Rs. 360
∴ C.I – S.I = Rs. (388 – 360) = Rs. 28