Question

How much time will it take for an amount of \[Rs.450\] to yield \[Rs.81\] as interest at \[4.5\% \] per annum of Simple Interest?
A) \[3\] yrs
B) \[3.5\] yrs
C) \[4\] yrs
D) \[4.5\] yrs

Answer 1

Hint:
Here, we will find the number of years. We will use the simple interest formula. We will substitute the given principal, interest and the rate of Interest in the simple interest formula and simplify it to find the number of years. Simple interest is defined as the interest calculated for the principal at a rate for a period of time.

Formula Used:
Simple Interest is given by the formula \[S.I. = \dfrac{{P \times n \times r}}{{100}}\] where \[S.I\] is the Simple Interest, \[P\] is the principal, \[r\] is the rate of Interest and \[n\] is the number of years.

Complete step by step solution:
We are given an amount of \[Rs.450\] which yields an interest of \[Rs.81\] at \[4.5\% \] per annum of Simple Interest.
Now, we will find the number of years for the Interest.
Let \[n\] be the number of years.
Substituting \[P = Rs.450\], \[r = 4.5\% \], \[S.I. = Rs.81\] and \[n = n\] in the formula \[S.I. = \dfrac{{P \times n \times r}}{{100}}\], we get
\[81 = \dfrac{{450 \times n \times 4.5}}{{100}}\]
Multiplying 100 on both sides, we get
\[8100 = 450 \times n \times 4.5\]
Again multiplying the terms, we get
\[8100 = 2025n\]
Dividing both sides by 2025, we get
\[ \Rightarrow n = \dfrac{{8100}}{{2025}}\]
 \[ \Rightarrow n = 4\] years
Therefore, the number of years for the given Simple interest is \[4\] years.

Thus, option (C) is the correct answer.

Note:
Simple interest is the term related to banking and financial sector. We should not get confused between simple interest and compound interest. The main difference between simple interest and compound interest is that simple interest is based only on the principal amount whereas compound interest is based on the principal amount and also the interest compounded for a period. Therefore, compound interest is called interest on interest,