Question

A sum of money put at \[11\% \] per annum amounts \[{\text{Rs 4491}}\] in \[2\] years \[3\] months. What will it amount to in \[3\] years at the same rate?

Answer 1

Hint: Here we will use the formula for calculating simple interest which is calculated on the principal portion of a loan or the original contribution to a savings account. The formula for calculating simple interest is as below:
\[{\text{S}}{\text{.I}} = \dfrac{{P \times r \times t}}{{100}}\] where
\[P = {\text{principal}}\],
\[r = {\text{rate of interest}}\] and
\[t = {\text{time}}\].
Also, simple interest always equals the difference between the final amount of value and the principal value.

Complete step by step solution:
Step 1: Assume that principal value is \[x\]. And as per the given information in the question \[t = 2{\text{ years }}3{\text{ months}}\] and \[r = 11\% \].
First, we will convert the given time into years as shown below:
\[t = 2\dfrac{3}{{12}}{\text{ yrs}}\] (because one year has twelve months)
By simplifying the above expression, we get:
\[ \Rightarrow t = \dfrac{9}{4}{\text{ yrs}}\]
Step 2: As we know the total amount equals the addition of the principal value and the interest in it. So, we get:
\[ \Rightarrow {\text{A}} = {\text{P}} + {\text{I}}\]
By substituting the value of
\[{\text{I}} = \dfrac{{P \times r \times t}}{{100}}\], in the above expression, we get:
\[ \Rightarrow {\text{A}} = {\text{P}} + \dfrac{{P \times r \times t}}{{100}}\]
By substituting the values of principal, rate, and time in the above expression, we get:
\[ \Rightarrow {\text{A}} = x + \dfrac{{x \times 11 \times \dfrac{9}{4}}}{{100}}\]
By solving the RHS side of the above expression, we get:
\[ \Rightarrow {\text{A}} = x + \dfrac{{99x}}{{400}}\]
By adding the terms in the RHS side of the above expression we get:
\[ \Rightarrow {\text{A}} = \dfrac{{400x + 99x}}{{400}}\]
By simplifying the RHS side of the above expression we get:
\[ \Rightarrow {\text{A}} = \dfrac{{499x}}{{400}}\]
By substituting the value of
\[{\text{A}} = 4491\] in the above expression as given in the question we get:
\[ \Rightarrow 4491 = \dfrac{{499x}}{{400}}\]
Multiplying \[400\] with \[4491\]as shown below:
\[ \Rightarrow 499x = 4491 \times 400\]
Bringing \[499\] into the RHS side and dividing it with \[4491\], we get the answer as below:
\[ \Rightarrow x = 9 \times 400\]
After doing the final multiplication above we get:
\[ \Rightarrow x = 3600\]
Step 3: Now the amount after three years will be as shown below:
\[ \Rightarrow {\text{A}} = 3600 + \dfrac{{3600 \times 11 \times 3}}{{100}}\]
By solving the multiplication and division in the RHS side of the above expression we get:
\[ \Rightarrow {\text{A}} = 3600 + 1188\]
By doing the final addition above we get:
\[ \Rightarrow {\text{A}} = {\text{Rs}}{\text{. }}4788\]

\[\because \] The amount after three years will be \[{\text{Rs}}{\text{. }}4788\].

Note: Students generally get confused about the amount and principal of the term. The amount is that value that comes after applying interest on the principal value i.e. Amount is always equal to the addition of simple interest and the initial principal value.
Also, here the customer is only paying the interest on principal value, there is no interest applicable on interest. So, you should use the simple interest formula instead of compound interest.