Question

A sum of \[\text{Rs}.\text{12},000\] is invested for 3 years at \[18\% \] per annum compound interest. Calculate the interest for the second year.
A) 2500
B) 2525
C) 2550
D) 2575

Answer 1

Hint:
Here we need to find the simple interest for 2 years. For that, we will first find the interest for 1 year using the formula and then we will find the amount. The amount that we will obtain will be the principal for second year. So we will again apply the formula of simple interest to get the answer.

Formula used:
\[SI = \dfrac{{P \times R \times T}}{{100}}\], where \[P\] is the principal, \[R\]is the rate of interest

Complete step by step solution:
Here we need to find the simple interest for 2 years.
It is given that:
Principal amount \[ = Rs.12,000\]
Time \[\left( T \right) = 3{\text{years}}\]
Rate of interest \[ = 18\% \]
Now, we will find the interest for 1 year using the formula.
So the time period will be 1 year.
Now, we will substitute the value of principal, rate of interest and the time in the formula of simple interest \[SI = \dfrac{{P \times R \times T}}{{100}}\]. Therefore, we get
\[ \Rightarrow SI = \dfrac{{12000 \times 18 \times 1}}{{100}}\]
On further simplifying the terms, we get
\[ \Rightarrow SI = Rs.2,160\]
Now, we will find the amount after the first year.
We know that the amount is equal to the sum of simple interest and the principal amount.
Therefore,
\[ \Rightarrow {\text{Amount}} = {\text{Principal}} + {\text{Simple interest}}\]
On substituting the value of principal and the simple interest in formula, we get
\[ \Rightarrow {\text{Amount}} = 12000 + 2160 = Rs14160\]
Now, the amount that we have calculated will become the principal amount for the second year.
Now, we will find the interest for the second year using the formula.
The formula of simple interest is
\[SI = \dfrac{{P \times R \times T}}{{100}}\]
Now, we will substitute the value of principal, rate of interest and the time in the formula of simple interest.
\[ \Rightarrow SI = \dfrac{{14160 \times 18 \times 1}}{{100}}\]
On further simplifying the terms, we get
\[ \Rightarrow SI = Rs.2548.80 \approx Rs.2550\]

Hence, the correct option is option C.

Note:
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. We should remember that in simple interest the interest and the principal has to be added to find the amount. However, in compound interest, the amount obtained after adding the principal and interest for first year becomes principal for second year. Simple interest benefits the consumers who always pay their loans on time or early each month. Short-term personal loans and auto loans are usually known as the simple interest loans.