Answer

Verified

445.2k+ views

**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.$1,78,512$

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

How do you graph the function fx 4x class 9 maths CBSE

Which are the Top 10 Largest Countries of the World?

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

The largest tea producing country in the world is A class 10 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE