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At what rate of simple interest any some amounts to 5/4 of the principal in 2.5 years​

User Velioglu
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To determine the rate of simple interest at which an amount grows to
\displaystyle\sf (5)/(4) of the principal in 2.5 years, we can use the formula for simple interest:


\displaystyle\sf I= P\cdot R\cdot T

where:


\displaystyle\sf I is the interest earned,


\displaystyle\sf P is the principal amount,


\displaystyle\sf R is the rate of interest, and


\displaystyle\sf T is the time period.

Given that the amount after 2.5 years is
\displaystyle\sf (5)/(4) of the principal, we can set up the equation:


\displaystyle\sf P+ I= P+\left((P\cdot R\cdot T)/(100)\right) =(5)/(4)\cdot P

Simplifying the equation, we get:


\displaystyle\sf (5P)/(4) =(P)/(1) +(P\cdot R\cdot T)/(100)

Now, let's solve for the rate of interest,
\displaystyle\sf R. We can rearrange the equation as follows:


\displaystyle\sf (5P)/(4) -(P)/(1) =(P\cdot R\cdot T)/(100)


\displaystyle\sf (5P-4P)/(4) =(P\cdot R\cdot T)/(100)


\displaystyle\sf (P)/(4) =(P\cdot R\cdot T)/(100)


\displaystyle\sf 100P =4P\cdot R\cdot T


\displaystyle\sf R =(100P)/(4P\cdot T)

Simplifying further, we find:


\displaystyle\sf R =(100)/(4\cdot T)

Substituting the given time period of 2.5 years, we get:


\displaystyle\sf R =(100)/(4\cdot 2.5)


\displaystyle\sf R =(100)/(10)


\displaystyle\sf R =10

Therefore, the rate of simple interest required for the amount to grow to
\displaystyle\sf (5)/(4) of the principal in 2.5 years is 10%.


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User Zaptree
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