Question

At the rate of interest of \[8\dfrac{1}{2}%\] p.a. a simple interest a sum of \[Rs.{ }4800\] will earn how much interest in \[2\] years \[3\] months?

Answer 1

Hint: According to question, rate of simple interest, principal amount, time all parameters are given on which the simple interest or the amount depends. To calculate the simple interest, we have a formula through which we can calculate interest and then add the interest in principal amount to get the net amount.

Formula used:
\[S.I.=\dfrac{P\times R\times T}{100}\] where, \[S.I.\] is Simple Interest
\[P\] is Principal amount
\[R\] is rate of interest
 \[T\] is the time period

Complete Step by Step Solution:
Given that,
Interest rate \[(R)=8\dfrac{1}{2}=\dfrac{17}{2}%\]
Time \[(T)=2yr+3months=2+\dfrac{3}{12}years=2+\dfrac{1}{4}=\dfrac{9}{4}years\]
(Since to convert months to years divide it by total months in one year that is divide by \[12\])
Principal amount \[(P)=Rs.4800\]
Now we know that to calculate the simple interest we use,
\[S.I.=\dfrac{P\times R\times T}{100}\]
Now substituting the given values in above formula
\[S.I.=\dfrac{4800\times \dfrac{17}{2}\times \dfrac{9}{4}}{100}\]
Now simplifying this
\[\Rightarrow 48\times \dfrac{17}{2}\times \dfrac{9}{4}\]
\[\Rightarrow 6\times 17\times 9\]
\[\Rightarrow 918\]
Thus, we have calculated the simple interest.

Hence, \[S.I.=Rs.918\]

Note:
First write down the given data and then recall the relation between what it has given and what we have to find. In this question we have used the simple formula for interest, note that the time period that we put in must be in years as the rate is given per year or annum. In this the interest is calculated with the same principal amount over the whole time period.