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Asked by snehakumar6321 | 14 Jan, 2023, 22:37: PM
answered-by-expert Expert Answer
Let P be principle and r is rate of interest per annum .
 
If first 2 year interest is Rs.272, then we have
 
begin mathsize 14px style p open parentheses 1 plus r over 100 close parentheses squared space minus space p space equals space 272 end style   ................................(1)
 
If first 3 year interest is Rs.434, then we have
 
begin mathsize 14px style p open parentheses 1 plus r over 100 close parentheses cubed space minus space p space equals space 434 end style   ................................(2)
 
By dividing eqn.(1) by eqn.(2) , we get after simplification as
 
begin mathsize 14px style fraction numerator open parentheses 1 plus begin display style r over 100 end style close parentheses squared minus 1 over denominator open parentheses 1 plus r over 100 close parentheses cubed minus 1 end fraction space equals space 272 over 434 end style  ..................................(3)
let us substitute x = ( r/100 ) in above equation and after further simplification, we get
 
begin mathsize 14px style fraction numerator x plus 2 over denominator x squared plus 3 x plus 3 end fraction space equals space 136 over 217 end style

From above expression, we get following quadratic expression
 
136 x2 + 191 x - 26 = 0
 
acceptable solution of above expression is x = 0.125
 
hence  r/100 = 0.125  or    r = 12.5
 
Hence rate of interest per annum is 12.5 %
 
Answered by Thiyagarajan K | 15 Jan, 2023, 09:37: AM
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