Question

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Answer 1

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 %.

Answer 2

Answer:

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