Question

Chaitanya borrows $Rs.\,45,000$ from a bank at $12%$ per annum. What amount will he pay to the bank if he repays the loan in (i) $6$ months (ii) $3$ months and (iii) $1\dfrac{1}{2}$ years?

Answer 1

Hint: Here we have been given a principal amount and rate at which Chaitanya borrows money from a bank. We have to find the money he has to give if he pays the money in the time given. Firstly we will write the formula of simple interest then as we know that time has to be in years we will change the months in years. Then we will substitute the value in the formula and get the simple interest. Finally we will add the principal amount and the interest value and get the desired answer.

Complete step-by-step solution:
Chaitanya borrows $RS.\,45,000$ from the bank at a rate of $12%$ per annum.
So we got the values as,
$P=Rs.\,45,000$
$R=12%$
Now we have to find the amount he has to pay to the bank so simple interest formula is as follows:
$S.I=\dfrac{P\times R\times T}{100}$
$S.I=\dfrac{45000\times 12\times T}{100}$
$S.I=5400\times T$…..$\left( 1 \right)$
(i) $6$ Months
So $T=6$ Months
As we know
$12$ Month’s $=1$ year
$1$ Month’s $=\dfrac{1}{12}$ year
$6$ Month’s $=\dfrac{6}{12}$ year
So, $T=\dfrac{1}{2}$ years
Substitute the above value in equation (1) we get,
$S.I=5400\times \dfrac{1}{2}$
$S.I=Rs.\,2700$
Amount $=P+S.I$
Amount $=45,000+2700$
Amount $=Rs.\,47,700$
He has to pay $Rs.\,47,700$ to the bank if he pays the money in $6$ months.
(ii) $3$ Months
So $T=3$ Months
$3$ Month’s $=\dfrac{3}{12}$ year
So, $T=\dfrac{1}{4}$ years
Substitute the above value in equation (1) we get,
$S.I=5400\times \dfrac{1}{4}$
$S.I=Rs.\,1350$
Amount $=P+S.I$
Amount $=45,000+1350$
Amount $=Rs.\,46,350$
He has to pay $Rs.\,46,350$ to the bank if he pays the money in $3$ months.
(iii) $1\dfrac{1}{2}$ Years
So $T=1\dfrac{1}{2}$ Years
 $\Rightarrow T=\dfrac{3}{2}$ Years
Substitute the above value in equation (1) we get,
$S.I=5400\times \dfrac{3}{2}$
$S.I=Rs.\,8100$
Amount $=P+S.I$
Amount $=45,000+8100$
Amount $=Rs.\,53,100$
He has to pay $Rs.\,53,100$ to the bank if he pays the money in $1\dfrac{1}{2}$ years.

Note: Simple interest is calculated on the principal amount at a particular rate for a given period of time. The principal amount is always the same for calculating simple interest. For example when we invest our money in any bank we are provided interest on the amount of money we have invested in the starting. The total money we get after a simple interest is the amount we invested plus the interest we get.