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# An amount of money fetches a simple interest of Rs.$4,320$ at the rate of $4$ percent per annum at the end of $6$ years. What is the principal amount?

Last updated date: 13th Jun 2024
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Hint: We will first discuss about the simple interest. Simple interest is the method to calculate the interest for money for a time period. Now the simple interest for a principal amount of $P$ at an interest rate of $R$ for a time period of $T$ years is
$SI=\dfrac{PRT}{100}$
So, from the above equation, the value of the principle amount is given by
$P=\dfrac{SI\times 100}{RT}$

Complete step-by-step solution:
Given that,
Simple interest $\left( SI \right)=4,320$
Rate of Interest $\left( R \right)=4$
Time period $\left( T \right)=6$years
From the formula of Simple Interest $SI=\dfrac{PRT}{100}$we have principle amount as
\begin{align} & P=\dfrac{SI\times 100}{RT} \\ & =\dfrac{4320\times 100}{4\times 6} \\ & =18000 \end{align}
Hence the principle amount is Rs.$18000$

Note: In the problem they mentioned simple interest. If they mentioned compounded interest then we had to use the formula $A=P{{\left( 1+\dfrac{R}{n} \right)}^{nt}}$ where $A$ is the Total amount, $P$ is the principle amount, $R$ is the interest rate in Decimals, $n$ is the number of times that the interest is compounded yearly, $t$ is the time period in years. So, assume the principle amount $P$ as $x$ and from given data $R=\dfrac{4}{100}=0.04$
$n$ is the number of times interest compounded yearly i.e. $n=1$ and time period is $t=6$years. Now the total amount is
\begin{align} & A=P{{\left( 1+\dfrac{R}{n} \right)}^{nt}} \\ & =x{{\left( 1+\dfrac{0.04}{1} \right)}^{1\left( 6 \right)}} \\ & =x{{\left( 1.004 \right)}^{6}} \\ & =1.0242x \end{align}
Now the compounded interest is given by
\begin{align} & CI=A-p \\ & =1.0242x-x \\ & =x\left( 1.0242-1 \right) \\ & =0.0242x \end{align}
But from the given data we have compounded interest as $CI=4,320$, then
\begin{align} & 0.0242x=4320 \\ & x=\dfrac{4320}{0.0242} \\ & =178512 \end{align}
So, the principle amount if the interest is compounded annually is Rs.$1,78,512$