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ICSE Class 9 Answered

difference between simple and compound interst on the same sum of money is 1/15 for three year is 184 determine the sum 
Asked by deepikanain005 | 14 Jul, 2018, 08:12: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space the space principal space amount space be space straight P.
Then comma space rate space of space interest space equals space straight r space equals space 1 over 15 space and space straight t space equals space 3 space years
rightwards double arrow Simple space Interest space equals space straight P cross times space straight r space cross times straight t space equals space straight P space cross times space 1 over 15 cross times space 3 space equals space straight P over 5 space and space
Compound space Interest space equals space straight P space left parenthesis space 1 space plus space straight r right parenthesis to the power of straight t space minus straight P space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space straight P space open parentheses 1 space plus space 1 over 15 close parentheses cubed space minus space straight P
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight P open square brackets open parentheses 1 space plus space 1 over 15 close parentheses cubed space minus 1 close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight P open curly brackets open parentheses 1 space plus space 1 over 15 space minus space 1 close parentheses open square brackets open parentheses 1 space plus space 1 over 15 close parentheses squared space plus open parentheses 1 space plus space 1 over 15 close parentheses cross times 1 space plus 1 squared space close square brackets close curly brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight P open square brackets 1 over 15 open parentheses 256 over 225 space plus space 16 over 15 space plus 1 close parentheses close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight P over 15 open square brackets fraction numerator 256 space plus 240 space plus space 225 over denominator 225 end fraction close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 721 straight P over denominator 3375 end fraction
Given colon space fraction numerator 721 straight P over denominator 3375 end fraction space minus straight P over 5 equals 184
rightwards double arrow fraction numerator 46 straight P over denominator 3375 end fraction space equals 184
rightwards double arrow straight P space equals fraction numerator 3375 cross times 184 over denominator 46 end fraction equals Rs. space 13 comma 500 end style
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