Question

If \[P = 5550\] and \[R = 12\% \] per annum simple interest, in what time will it amount to Rs. 6882?

Answer 1

Hint: Here, we need to find the time period. We will use the formula for simple interest to form a linear equation in one variable. Then, we will solve this equation to find the value of the time period in which Rs. 5550 amounts to Rs. 6882 at \[12\% \] per annum simple interest.

Formula used:
We will use the following formulas:
1.The simple interest is given by \[S.I. = \dfrac{{P \times R \times T}}{{100}}\], where \[P\] is the principal amount, \[R\] is the rate of interest, and \[T\] is the time period.
2.The amount is the sum of the principal amount and the interest. It is given by the formula \[A = P + S.I.\], where \[P\] is the principal amount and \[S.I.\] is the simple interest.


Complete step-by-step answer:
Let \[T\] be the time period in which the principal amounts to Rs. 6882 at \[12\% \] per annum.
We will use the formula for simple interest to form an equation in terms of \[T\].
Substituting \[P = 5550\] and \[R = 12\] in the formula \[S.I. = \dfrac{{P \times R \times T}}{{100}}\], we get
\[ \Rightarrow S.I. = \dfrac{{5550 \times 12 \times T}}{{100}}\]
Multiplying the terms, we get
\[ \Rightarrow S.I. = \dfrac{{66600T}}{{100}} = 666T\]
The amount is the sum of the principal amount and the interest. It is given by the formula \[A = P + S.I.\], where \[P\] is the principal amount and \[S.I.\] is the simple interest.
It is given that the amount is Rs. 6882.
Substituting \[A = 6882\], \[P = 5550\], and \[S.I. = 666T\] in the formula, we get
\[ \Rightarrow 6882 = 5550 + 666T\]
We can observe that this is a linear equation in one variable in terms of \[T\].
We will solve this equation to find the value of \[T\], and hence, the time period.
Subtracting 5550 from both sides of the equation, we get
\[\begin{array}{l} \Rightarrow 6882 - 5550 = 5550 + 666T - 5550\\ \Rightarrow 1332 = 666T\end{array}\]
Dividing both sides of the equation by 666, we get
\[ \Rightarrow \dfrac{{1332}}{{666}} = \dfrac{{666T}}{{666}}\]
Therefore, we get
\[ \Rightarrow T = 2\]
Thus, we get the time period as 2 years.
\[\therefore \] If \[P = 5550\] and \[R = 12\% \] per annum simple interest, the principal will amount to Rs. 6882 in 2 years.

Note: Simple interest is the interest paid on a certain amount at a certain interest rate for a particular time period. The total amount is found out by adding the principal amount to the interest accumulated. Simple interest is different from compound interest. In compound interest, the principal of the second year is the total amount of first-year i.e. principal of the first year with the interest accumulated in the first year. In simple interest, the principal remains the same for each year.