Question

There is a 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs.12,000 after 3 years at the same rate?
A.Rs.2160
B.Rs.3120
C.Rs.3972
D.Rs.6240
E.None of these

Answer 1

Hint: The given question is related to simple interest and compound interest. Using the formula of simple interest, first, find the principal amount. Then, using the formula for compound interest, calculate the interest.

Complete step by step answer:
The simple interest can be defined as the principal amount of loan or deposit, a person makes into their bank account.
The formula for simple interest is:
Simple Interest (SI) = Principal amount (P) x Interest Rate (R) x Time of loan or deposit (T) in years.
In the question, it is given that there is an increase of 60% in an amount in 6 years at simple interest.
But, here the Principal amount (P) is not given. So, let us assume it to be Rs.P
So, as there is a 60% increase in P. Therefore, the simple interest will be 60% of Rs.P
$\begin{align}
  & \Rightarrow SI=60\%ofP \\
 & \Rightarrow SI=\dfrac{60}{100}\times P \\
\end{align}$
(T) is 6 years given and (R) is unknown.
$\begin{align}
  & \therefore SI=\dfrac{P\times R\times T}{100} \\
 & \Rightarrow \dfrac{60\times P}{100}=\dfrac{P\times R\times 6}{100} \\
 & \Rightarrow R=10 \\
\end{align}$
Hence, the rate of interest (R) is 10% per annum.
Now, we have to find the compound interest of Rs.12,000 after 3 years at the same rate.
The formula to calculate the compound interest is $A=P\times {{\left( 1+\dfrac{R}{100} \right)}^{n}}$
Here, (A) is the final Amount, (P) is the Principal Amount, (R) is the Rate of Interest, (n) is the number of years.
So, now we will calculate (A):
$\begin{align}
  & A=P\times {{\left( 1+\dfrac{R}{100} \right)}^{n}} \\
 & \Rightarrow A=12000\times {{\left( 1+\dfrac{10}{100} \right)}^{3}} \\
 & \Rightarrow A=12000\times {{\left( 1+\dfrac{10}{100} \right)}^{3}}=12000\times {{\left( \dfrac{110}{100} \right)}^{3}}=12000\times {{\left( \dfrac{11}{10} \right)}^{3}}=12\times {{11}^{3}}=15972 \\
\end{align}$
Hence, (A) i.e. the final amount is Rs.15972.
Compound Interest (CP) = (A) – (P)
So, here (A) is Rs.15972 and (P) is Rs.12000
$\Rightarrow CP=Rs.15972-Rs.12000=Rs.3972$
Hence, the option (c) is correct.

Note: In this question, the calculation part is not very large, but there can be questions like this which will involve solving large calculations, especially in the case of decimal figures. So, there can be a possibility of mistakes. Also, the possibility of mistake can be not thinking of the appropriate formula, or not linking the question to that particular concept while solving. You are advised to follow every step properly to avoid calculation mistakes and it will also save you time.