Question

Find the simple interest and amount when \[\text{Principal}=Rs.\text{ }2650\], \[\text{rate}=8%\] p.a. and \[\text{time}=2\dfrac{1}{2}years\].

Answer 1

Hint: The first part we need to find is the simple interest generated annually for \[2\dfrac{1}{2}\text{ }years\] at \[8%\] per annum and after that we need to find the amount by adding the principal to simple interest.
To find the simple interest we use the formula:
\[S.I.=\dfrac{P\times R\times T}{100}\]
To find the amount we use the formula:
\[A=S.I.+P\]
where \[S.I.,A,P,T\] and \[R\] is simple interest, amount, principal, time (in years) and rate percentage respectively.

Complete step-by-step answer:
Now we put the values in the formula to find amount, \[P=Rs.2650\], \[T=2\dfrac{1}{2}years\], \[R=8%\] as:
\[S.I.=\dfrac{P\times R\times T}{100}\]
\[S.I.=\dfrac{2650\times 8\times 2\dfrac{1}{2}}{100}\]
\[S.I.=\dfrac{2650\times 8\times \dfrac{5}{2}}{100}\]
\[S.I.=\dfrac{2650\times 4\times 5}{100}\]
\[S.I.=Rs.\text{ }530\]
Now to find the amount we add the principal with simple interest:
\[A=S.I.+P\]
\[A=Rs.\text{ 530}+Rs.\text{ 2650}\]
\[A=Rs.\text{ 3180}\]
Hence, the Amount \[=Rs.\text{ 3180}\] and Simple Interest \[=Rs.\text{ }530\].

Note: Another method to find the amount and the simple interest is to first amount by using the formula as \[A=P\left[ \left( \dfrac{R\times T}{100} \right)+1 \right]\] and then subtract the amount with principal to find the simple interest by \[S.I.=A-P\].