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# Harsha borrowed Rs.5000 to purchase a sewing machine from a women savings bank at $5\%$ rate of compound interest, so at the end of $3$ years how much amount will she pay?

Last updated date: 17th Sep 2024
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Hint: In this question, we have to evaluate the compound interest amount calculated for a specific period for a specific rate of interest. They give the principal amount, rate of interest, and period to find the compound interest.
We know the formula of compound interest putting all the given amount, rate, and time we will get the required solution.

Formula used:
Compounded amount is $A$,
$A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$ where
$P$ is the principal amount,
$r$ is the rate of interest,
$n$ is the period.

Complete step by step answer:
It is given that Harsha borrows $Rs.{\text{ }}5000$ to purchase a sewing machine from a women savings bank at $5\%$ rate of compound interest.
We need to find out the amount she will pay at the end of $3$ years.
Here,
$P =$Principal amount$= Rs.{\text{ }}5000$.
$r =$Rate of interest$= 5\%$
$n =$Time period$= 3$years
Applying the compound interest formula we get,
$\Rightarrow A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$
Substituting the values of $A,{\text{ }}P,{\text{ }}r,{\text{ }}n$ into the compound interest formula,
$\Rightarrow A= 5000{\left( {1 + \dfrac{5}{{100}}} \right)^3}$
Dividing the term $\dfrac{5}{{100}}$ we get,
$\Rightarrow A= 5000 \times {\left( {1 + \dfrac{1}{{20}}} \right)^3}$
Simplifying the terms we get,
$\Rightarrow A = 5000 \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}}$
$\Rightarrow A = 5788.12$

$\therefore$ The amount she will pay at the end of $3$ years is $Rs.{\text{ }}5788.12$.

Note:
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.