Question

A simple interest on the principal amount of \[Rs.450\] leads the final amount to \[Rs.495\] in 2 years. In what time the principle leads to \[Rs.820\] final amount of \[Rs.943\] at the same rate?
a) \[3years\]
b) \[2years\]
c) \[4years\]
d) \[6years\]

Answer 1

Hint: We should know the different formulas like:
Simple Interest, \[S.I = \dfrac{{Principle \times Rate \times Time}}{{100}} = \dfrac{{P \times T \times R}}{{100}}\],Total amount, \[A = P + S.I\;\]
Rate of interest, \[R = \dfrac{{\left( {S.I \times 100} \right)}}{{P \times T}}{\text{ }}\],Time taken, \[T = \dfrac{{\left( {S.I \times 100} \right)}}{{P \times R}}{\text{ }}\].
Rate of interest is always in percentage per annum, until it is mentioned. If rate is given per month or any unit, we should convert it in per annum.

Complete step-by-step solution:
The principal amount of a loan or deposit is the basis for simple interest. Simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent.
we have given principal amount is the basic amount deposited \[P = 450\]
and final amount is the amount received after the tenure \[A = 495\]
similarly, T is the time during which our money is deposited \[T = 2\]
we will calculate the simple interest using formula
\[A = P + S.I\;\]
We substitute their value
\[495 = 450 + S.I\]
\[\Rightarrow S.I = 495 - 450\]
\[\Rightarrow S.I = 45\]
We will find the rate of interest (R) by using,
\[R = \dfrac{{\left( {S.I{\text{ }} \times {\text{ }}100} \right)}}{{P \times T}}{\text{ }}\]
$\Rightarrow R = \dfrac{{45 \times 100}}{{450 \times 2}}$
Now, by solving it, we get\[R = 5\% \]
Now we have \[P = 820\], \[A = 943\], \[R = 5\% \]
So, by using,
\[A = P + S.I\;\]
\[\Rightarrow S.I = 943 - 820\]
\[\Rightarrow S.I = 123\]
We will calculate time using
\[T = \dfrac{{\left( {S.I \times 100} \right)}}{{P \times R}}{\text{ }}\]
$\Rightarrow T = \dfrac{{123 \times 100}}{{820 \times 5}}$
$\Rightarrow T = 3$
Time taken =\[3\]years, and the correct option for the answer is option a)\[3\]years.

Note: The principal amount of a loan or deposit is the basis for simple interest. Simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. while, Compound interest accrues and is added to the accumulated interest of previous periods; it includes interest on interest.