On a certain Principal if the Simple interest for two years is Rs. 2400 and Compound interest for the two years is Rs. 2544, what is the rate of Interest?
1). 12 percentThe formula for annual compound interest, including principal sum, is: $(CI\\; = \\;P{\\left( {1\\; + \\;\\frac{r}{{100\\; \\times \\;n}}} \\right)^{nt}} - P)$
\r\n\r\nWhere:
\r\n\r\nCI = Compound InterestP = the principal investment amount (the initial deposit or loan amount)r = the annual interest rate (decimal)n = the number of times that interest is compounded per yeart = the number of years the money is invested or borrowed for
\r\n\r\nHere n = 2
\r\n\r\nLet the principal be P
\r\n\r\nSI = (P × r × 2)/100 = 2400
\r\n\r\nPr = 120000
\r\n\r\nCI = P(1 + r/100)2 – P = 2544
\r\n\r\nP(1 + r2/10000 + 2r/100) – P = 2544
\r\n\r\n(Pr) × r/10000 + Pr/50 = 2544
\r\n\r\n120000r/10000 + 2400 = 2544
\r\n\r\nr = 12%
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