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maths

Asked by snehakumar6321 | 14 Jan, 2023, 10:37: PM

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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