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. 25. If the interest were compounded half yearly, the difference in two interests would be:
S.I – C.I = (P r²)/((100)²) 25 = (P (10)²)/((100)²) P = (25 ×100 ×100)/(10 × 10 ) P = Rs 2,500 S.I = (2500×10 ×2)/(100 ) = Rs 500 C.I = 2,500(1+ 5/100)^4- 2,500 C.I = 2,500 ×105/100×105/100×105/100×105/100 – 2,500 = Rs 538.76 ∴ Required difference = 538.76 – 500 =Rs 38.76 Alternate method: S.I – C.I (for annually basis in %) = r^2/100 % = 10^2/100 % = 1% which is given= RS. 25 But when it is half yearly, r will be 5% ad it will be applicable for 4 years. For 1 year , CI = 5 + 5 + (5×5)/100=10.25% For 2 years , CI = 10.25+10.25 +(10.25×10.25)/100 = 20.5+(41/4×41/4)/100 = (20.5+1681/1600)% & SI for 2 years on half yearly = 5+5+5+5 = 20% So CI – SI = 20.5 + 1681/1600 - 20 = 1681/1600+0.5=2481/1600% So Now 1% = 25 So 2481/1600% = 25×2481/1600% = 38.76 Rs.
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