Question

What sum of money will produce \[Rs.28,600\] as an interest in \[3\] years and \[3\]months at \[2.5%\]p.a. simple interest?
(A) \[Rs.3,52,00\]
(B) \[Rs.3,22,00\]
(C) \[Rs.3,42,00\]
(D) \[Rs.3,32,00\]

Answer 1

Hint: Amount is the total amount of money that we pay at the end after taking the loan from the bank or from somewhere else. So the amount will be calculated by adding simple interest with the original amount and simple interest is calculated by multiplying the principal amount with the rate of interest and the time.

Complete step-by-step solution:
Before solving the problem on simple interest, let us first understand that what is simple interest. Suppose, if we buy the loan from the bank then we also have to return it. A loan is an amount that a borrower takes from the bank at the time of need and when you return that loan to the bank then you have to return it with some extra amount of money. So the amount that we return to the bank after a certain period will be paid as the sum of simple interest and the original amount that we have taken from the bank.
Bank also provides simple interest to us if we invest our money in banks.
So simple interest is then obtained by multiplying the rate of interest with the principal amount. The rate of interest is given in the form of percentage and period will be calculated in years.
The formula for simple interest is given as shown below.
\[S.I=P\times R\times t\]…….eq(1)
Where S.I is the simple interest, ‘P’ represents the principle amount, ‘R’ is the rate of interest, and ‘t’ is the time taken.
So in the above question, we have to find the principal amount that will produce an interest of \[Rs.28,600\], at the rate of \[2.5%\]p.a for the time of \[3\] years and 3 months.
So here,
\[S.I=28,600\]
\[R=\dfrac{2.5}{100}\]
\[t=3+\dfrac{3}{12}years\]
\[\Rightarrow t=\dfrac{39}{12}years\]
We have to find the value of P. So on putting all these values in eq(1), we get
\[S.I=P\times R\times t\]
\[\Rightarrow 28600=P\times \dfrac{2.5}{100}\times \dfrac{39}{12}\]
On solving this we get.
\[P=\dfrac{28600\times 100\times 12\times 10}{25\times 39}\]
\[\Rightarrow P=3,52,000\]
So the principal amount will be \[Rs.3,52,000\]. Hence the correct answer is (A) \[Rs.3,52,000\] .

Note: Interest is of two types- simple interest and compound interest. Compound interest is more complicated as compared to simple interest and also you have to pay more money in compound interest. In simple interest, the amount of loan and the rate of interest does not change over time but in compound interest, the interest payment is added to the principal over time.