Question

The sum required to earn a monthly interest of \[Rs.1200\] at \[18\% \] p.a. simple interest is

A.\[Rs.50000\]

B.\[Rs.60000\]

C.\[Rs.80000\]

D.None of above

Answer 1

Hint: As we know that the formula of simple interest is \[S.I = \dfrac{{P \times R \times N}}{{100}}\], and here we have to find out the principle amount that is required to have the simple interest \[Rs.1200\] at \[18\% \] p.a. with monthly interest. So, here the time period will be one month and we have to convert it in the form of years and use it in the above formula.

Complete step-by-step answer:
As the given is, we have to earn a monthly interest of \[Rs.1200\] at \[18\% \] p.a. simple interest.
So, one month will be \[\dfrac{1}{{12}}\]years as in one year there are \[12\] months.
We have,\[SI = 1200\]
\[R = 18\% \]
\[N = \dfrac{1}{{12}}\]
So, using the formula of \[S.I = \dfrac{{P \times R \times N}}{{100}}\]
On Substituting the values, we get,
\[ \Rightarrow \]\[1200 = \dfrac{{P \times 18 \times \dfrac{1}{{12}}}}{{100}}\]
On cross-multiplying and simplifying the terms, we get,
\[ \Rightarrow \]\[P \times 18 \times \dfrac{1}{{12}} = 120000\]
On simplifying we get,
\[ \Rightarrow \]\[P \times \dfrac{3}{2} = 120000\]
Again, cross-multiplying, we get,
\[ \Rightarrow \]\[P = 120000 \times \dfrac{2}{3}\]
Hence, on simplification we get
\[ \Rightarrow \]\[P = 40000 \times 2 = Rs.80,000\]
Hence the sum required to earn a monthly interest of \[Rs.1200\] at \[18\% \] p.a. simple interest is \[Rs.80000\].
Hence, option (C) is the correct answer.

Note: Use the given quantities in the formula of \[S.I = \dfrac{{P \times R \times N}}{{100}}\]without any mistake.
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments