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9 Ashok borrowed 12,000 at some rate percent compound interest. After a year, he paidback * 4,000. If compound interest for thesecond year be *920, find :(i) the rate of interest charged(ii) the amount of debt at the end of thesecond year. |
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Answer» Principal (i) = 12000 Rs After 1 year he paid back Rs 4000 Let the rate of interest be r Hence, the principle after 1 year= 12000(1+r/100)-4000 Now it is given that C.I for 2nd year = 920 Hence, {12000(1+r/100)-4000}(1+r/100) = {12000(1+r/100)-4000 +920} => (1+r/100) = {12000(1+r/100)-4000 +920}/{12000(1+r/100)-4000} => (1+r/100) = {8920+120r}/{8000+120r} => r/100 = {8920+120r}/{8000+120r} - 1 => r/100 = 920/8000+120r => 120r^2+8000r-92000 = 0 => 3r^2+200r-2300=0 => 3r^2 -30r+230r-2300=0 => 3r(r-10) + 230(r-10)=0 => (3r+230)(r-10)=0 Since rate cannot be negative Hence r = 10 Therefore rate of interest =10% 2. Now initial principle = 12000 C.I for 1st year = 12000(1+10/100)-12000 = 13200-12000 = 1200 C.I. for 2nd year = 920 Hence sum of principle and interest of both years=12000+1200+920=14120 But he paid back 4000 Hence amount of debt at the end of 2nd year = 14120 - 4000 = 10120 Rs. |
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