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Find the compound interest on \[{\text{Rs}}.48000\] for \[2{\text{ yrs}}\] compounded annually at \[2\dfrac{1}{2}\% \] per annum.

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Last updated date: 17th Jun 2024
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Answer
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Hint: Here we will be using the formula of compound interest which states as below:
\[A = P{\left( {1 + \dfrac{r}{n}} \right)^{nt}}\] , where
\[A = {\text{final amount}}\],
\[P = {\text{initial principal balance}}\],
\[r = {\text{rate of interest}}\],
\[n = {\text{no}}{\text{.of time interest applied }}\] and
\[t = {\text{number of time periods}}\].

Complete answer:
Step 1: As given in the question
\[P = 48000\],
\[r = \dfrac{5}{2}\% \] ,
\[t = 2{\text{ yrs}}\] and
\[n = 1\]. By substituting these values in the formula
\[A = P{\left( {1 + \dfrac{r}{n}} \right)^{nt}}\]we get:
\[A = 48000{\left( {1 + \dfrac{{5/2}}{1}} \right)^{1 \times 2}}\]
By solving inside the brackets in the RHS side of the above expression, we get:
\[ \Rightarrow A = 48000{\left( {1 + 0.025} \right)^2}\]
By doing addition inside the brackets in the RHS side of the above expression, we get:
\[ \Rightarrow A = 48000{\left( {1.025} \right)^2}\]
By solving the powers and multiplying
\[1.025 \times 1.025\], on the RHS side we get:
\[ \Rightarrow A = 48000\left( {1.050625} \right)\]
After doing the final multiplication in the RHS side of the above expression, we get:
\[ \Rightarrow A = {\text{Rs}}.{\text{ }}50430\]
Step 2: Now, as we know interest equals the subtraction of principal amount from total amount i.e. \[ \Rightarrow {\text{Interest}} = A - P\].
By substituting the values of \[P = 48000\] and \[A = 50430\] in the RHS side of the above expression we get:
\[ \Rightarrow {\text{Interest}} = 50430 - 48000\]
By doing the subtraction in the RHS side of the above expression we get:
\[ \Rightarrow {\text{Interest}} = {\text{Rs}}{\text{. }}2430\]

Interest amount is \[{\text{Rs}}{\text{. }}2430\].

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.