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Answer» Question :Peter invested a certain sum of money in a simple interest bond WHOSE value grew to Rs. 300 at the end of 3 years, and to Rs. 400 st the end of another 5 years. What was the RATE of interest? ANSWER :Let the sum of money invested i.e Principal be Rs. P an Rate of interest be R % . At the end of 3 years sum amounts to Rs. 300 Time ( T ) = 3 year Amount = Rs. 300 ⇒ P( 1 + TR / 100 ) = 300 ⇒ P( 1 + 3R / 100 ) = 300 ⇒ P{ ( 100 + 3R ) / 100 } = 300 -- ( EQUATION 1 ) At the end of another 5 years sum amounts to Rs. 400 Time ( T ) = 3 years + 5 years = 8 years Amount = Rs. 400 ⇒ P( 1 + TR / 100 ) = 400 ⇒ P( 1 + 8R / 100 ) = 400 ⇒ P{ ( 100 + 8R ) / 100 } = 400 -- ( Equation 2 ) Dividing Equation 1 by Equation 2 ⇒ P{ ( 100 + 8R ) / 100 } / P{ ( 100 + 3R ) / 100 } = 400 / 300 ⇒ ( 100 + 8R ) / ( 100 + 3R ) = 4 / 3 ⇒ 300 + 24R = 400 + 12R ⇒ 24R - 12R = 400 - 300 ⇒ 12R = 100 ⇒ 3R = 25 ⇒ R = 25/3 = 8.33 % Therefore the Rate of interest was 25/3 % or 8.33 %. |
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