Question

Calculate the compound interest on Rs. 6000 at \[10\% \] per annum for two years.

Answer 1

Hint:
Here, we will substitute the given values in the formula for amount and find the amount. Then we will subtract the principal amount from the amount we obtained to find the compound interest. Compound interest is defined as the interest calculated for the principal and the interest accumulated over a period of years before.

Formula Used:
We will use the following formula:
1) If the amount is compounded annually, then the amount is given by \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}\] where \[A\] is the amount, \[P\] is the principal, \[R\] is the rate of Interest and \[t\] is the number of years.
2) Compound Interest is given by the formula \[C.I. = A - P\] where \[A\] is the amount, \[P\] is the principal.

Complete Step by Step Solution:
We are given a principal of Rs. 6000 at \[10\% \] per annum for two years.
Now, we will find the amount of compound interest.
Substituting \[P = 6000\], \[R = 10\% \] and \[t = 2{\rm{years}}\] in the formula \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}\], we get
\[A = 6000{\left( {1 + \dfrac{{10}}{{100}}} \right)^2}\]
Dividing numerator and denominator by 10 inside the bracket, we get
\[ \Rightarrow A = 6000{\left( {1 + \dfrac{1}{{10}}} \right)^2}\]
Taking LCM inside the bracket, we get
\[ \Rightarrow A = 6000{\left( {1 \times \dfrac{{10}}{{10}} + \dfrac{1}{{10}}} \right)^2}\]
\[ \Rightarrow A = 6000{\left( {\dfrac{{10}}{{10}} + \dfrac{1}{{10}}} \right)^2}\]
Adding the terms in the bracket, we get
\[ \Rightarrow A = 6000{\left( {\dfrac{{11}}{{10}}} \right)^2}\]
By squaring and simplifying, we get
\[ \Rightarrow A = 6000\left( {\dfrac{{121}}{{100}}} \right)\]
Multiplying the terms, we get
\[ \Rightarrow A = 60 \times 121\]
\[ \Rightarrow A = 7260\]
Now, we will find the compound interest.
Substituting in \[P = 6000\] and \[A = 7260\] in the formula \[C.I = A - P\], we get
\[C.I = 7260 - 6000\]
Subtracting the terms, we get
\[ \Rightarrow C.I = 1260\] .

Therefore, the compound interest on Rs. 6000 is Rs. 1260.

Note:
We might make a mistake by finding out simple interest instead of compound interest. The difference between simple interest and compound interest is that in simple interest is based only on the principal amount that remains the same for every year. Whereas in compound interest, the principal amount changes as the interest of every year is added to the principal amount, and the compound interest is calculated on the increased principal amount.
We might think of the amount to the compound interest and leave the answer at that. We need to keep in mind that compound interest is found out by subtracting the principal from the amount.