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(a) The rate of interest per annum.

(b) The amount at the end of 3 years.

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Before starting with the question, let us know about interest.

Interest in the financial term is the amount that a borrower pays to the lender along with the repayment of the actual principal amount.

Broadly, there are two kinds of interest, first is the simple interest, and the other is the compound interest.

Let us apply the formula $A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}$ , for the first 2 years. For the first 2 years, amount A is Rs. 6272, principal P is Rs. 5000 and time t is 2 years. So, if we put this in formula, we get

$6272=5000{{\left( 1+\dfrac{r}{100} \right)}^{2}}$

$\Rightarrow \dfrac{6272}{5000}=\dfrac{3136}{2500}={{\left( 1+\dfrac{r}{100} \right)}^{2}}$

Taking root of both the side gives:

$\sqrt{\dfrac{3136}{2500}}=\left( 1+\dfrac{r}{100} \right)$

$\Rightarrow \dfrac{56}{50}=\left( 1+\dfrac{r}{100} \right)$

$\Rightarrow \dfrac{r}{100}=\dfrac{6}{50}$

$\Rightarrow r=\dfrac{6}{50}\times 100=12\%$

Therefore, the rate of interest is 12%.

Now we will again use the same formula for 3 years. For this case, P=5000, r=12 and t=3.

$A=5000{{\left( 1+\dfrac{12}{100} \right)}^{3}}$

$A=5000{{\left( \dfrac{112}{100} \right)}^{3}}=\dfrac{5000\times 112\times 112\times 112}{100\times 100\times 100}=Rs.\text{ }7024.64$

Therefore, the amount at the end of 3 years is Rs. 7024.64.

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