Question

Find the compound interest on \[{\text{Rs}}{\text{. 800}}\] for \[2{\text{ years}}\] at \[5\% \] per annum.
A. \[{\text{Rs}}{\text{. 82}}\]
B. \[{\text{Rs}}{\text{. 882}}\]
C. \[{\text{Rs}}{\text{. 72}}\]
D. \[{\text{Rs}}{\text{. 92}}\]

Answer 1

Hint: Here we will be using the formula for calculating compound interest as shown below:
\[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\] where
\[A = {\text{final amount}}\],
\[P = {\text{initial principal balance}}\],
\[r = {\text{rate of interest}}\],
\[n = {\text{no}}{\text{.of time interest applied }}\].

Complete step-by-step answer:
Step 1: It is given in the question that
\[P = 800\],
\[r = 5\% \] and
\[n = 2\].
Assume that compound interest equals \[x\]. Also, we know that \[A = {\text{C}}{\text{.I}} + P\].
By substituting these values in the formula:
\[A = P{\left( {1 + \dfrac{r}{n}} \right)^{nt}}\], we get:
\[x + 800 = 800{\left( {1 + \dfrac{5}{{100}}} \right)^2}\] ……………………… (1)
Step 2: By solving the brackets in the RHS side of the above equation we get:
\[ \Rightarrow x + 800 = 800{\left( {1 + \dfrac{1}{{20}}} \right)^2}\]
By replacing the term \[{\left( {1 + \dfrac{1}{{20}}} \right)^2} = 1 + \dfrac{1}{{400}} + 2 \times 1 \times \dfrac{1}{{20}}\] in the above equation we get:
\[ \Rightarrow x + 800 = 800\left( {1 + \dfrac{1}{{400}} + 2 \times 1 \times \dfrac{1}{{20}}} \right)\]
By solving inside the brackets, we get:
\[ \Rightarrow x + 800 = 800\left( {1 + \dfrac{1}{{400}} + \dfrac{1}{{10}}} \right)\]
By doing addition inside the brackets of the RHS side of the equation we get:
\[ \Rightarrow x + 800 = 800\left( {\dfrac{{4000 + 10 + 400}}{{400 \times 10}}} \right)\]
By solving the brackets in the RHS side of the above equation we get:

\[ \Rightarrow x + 800 = 800\left( {\dfrac{{441}}{{400}}} \right)\]
Step 3: Solving the RHS side of the equation
\[x + 800 = 800\left( {\dfrac{{441}}{{400}}} \right)\] by dividing we get:
\[ \Rightarrow x + 800 = 882\]
Bringing
\[800\] into the RHS side and after doing subtraction we get:
\[ \Rightarrow x = {\text{Rs}}{\text{. }}82\]

\[\because \]Compound interest will be equal to \[{\text{Rs}}{\text{. }}82\].

Note:
Students need to remember the difference between the Simple interest and compound interest formulas. Simple interest is calculated on the principal amount. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, which is known as interest on interest.
Also, students need to know that the formula which we are using is for calculating the amount, not compound interest. Compound interest is the difference between the amount and principal value.