Question

Find the simple interest on: - Rs. 1400 for $3\dfrac{1}{2}$ years at $4\dfrac{1}{2}\%$ per annum.

Answer 1

Hint: Consider Rs. 1400 as the principal amount (P), $3\dfrac{1}{2}$ years as time (T) and $4\dfrac{1}{2}\%$ per annum as rate of interest (R) per year. Convert the mixed fractions into the improper fractions by using the conversion relation $a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{b}$ to simplify. Now, use a simple interest formula given as S.I = $\dfrac{P\times R\times T}{100}$ to get the answer. Here, S.I is the Simple Interest.

Complete step by step answer:
Here we have been asked to find the simple interest on Rs. 1400 for the time $3\dfrac{1}{2}$ years and rate of interest is $4\dfrac{1}{2}\%$ per annum. First let us convert the given mixed fraction into the improper fractions for the calculation.
Now, we know that the simple interest on a Principal amount (P) charged over the time (T) years at the rate of interest being (R) % per annum is given as S.I = $\dfrac{P\times R\times T}{100}$. So, in the above question we have to find the interest on Rs. 1400 for $3\dfrac{1}{2}$ years at $4\dfrac{1}{2}\%$ per annum, therefore we have,
$\Rightarrow $ P = Rs. 1400, R = $4\dfrac{1}{2}\%$ and T = $3\dfrac{1}{2}$ years
Converting the mixed fractions into the improper fractions by using the relation $a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{b}$ we get,
$\Rightarrow $ P = Rs. 1400, R = $\dfrac{9}{2}\%$ and T = $\dfrac{7}{2}$ years
Substituting the values in the formula of Simple Interest we get,
$\begin{align}
  & \Rightarrow S.I=\dfrac{1400\times \dfrac{9}{2}\times \dfrac{7}{2}}{100} \\
 & \therefore S.I=220.5 \\
\end{align}$
Hence, the Simple Interest on the given amount is Rs. 220.5.

Note: Note that if you are asked to calculate the total amount to be paid then you have to add the obtained interest with the principal amount to get the answer. The reason is that the total amount to be returned is the sum of principal amount and the interest calculated. Remember that the time must be in years or if it is in months then we have to convert it in years before substituting it in the formula.