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12,000 is invested for 1.5 years at C.I. If 15,972 is received at the end of this period,find the rate of interest per annum. |
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Answer» R = 21 % R = 20.64 % Step-by-step EXPLANATION: LET say RATE of interest = R Interest for 1st Year = 12000 * R * 1 /100 = 120 R Amount after 1 YEARS = 12000 + 120R interest for next 1/2 years = (12000 + 120R) * (1/2) R /100 = (120 + 1.2R)R/2 = 60R + 0.6R² 120 R + 60R + 0.6R² = 15972 - 12000 => 0.6R² + 180R = 3972 => R² + 300R = 6620 => R² + 300R - 6620 = 0 => R = 20.64 % But if We calculate Amount = P (1 + R/100)ⁿ => 15972 = 12000 ( 1 + R/100)^(3/2) => 1.331 = ( 1 + R/100)^(3/2) => 1.1 = √(1 + R/100) => 1.21 = 1 + R/100 => R/100 = 0.21 => R = 21 % |
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