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We know that the general formula for calculating the compound interest is given by the equation

\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}.............(1)\]

Here A denotes the Amount received after n years when Principal P has compounded annually for n years with the rate of interest denoted as R.

Let us take the amount received for the rate of interest 3% to be denoted by $A_1$.

Here ${P_1} = 10000,{R_1} = 5\% ,{n_1} = 2years$

Now we will put it in equation (1), the formula becomes

${A_1} = {P_1}{\left( {1 + \dfrac{{{R_1}}}{{100}}} \right)^{{n_1}}}................(2)$

Hence by substituting the values, we get

${A_1} = 10000{\left( {1 + \dfrac{3}{{100}}} \right)^2}$

$A_1^{} = 10609.$

Now similarly we let the amount received for the rate of interest 4% be denoted as ${A_2}$

Here ${P_2} = 10000,{R_2} = 4\% ,{n_2} = 2years$

Now the formula to calculate $A_2$ is given by the equation

${A_2} = {P_2}{\left( {1 + \dfrac{{{R_2}}}{{100}}} \right)^{{n_2}}}..................(3)$

Hence by substituting the values we get

${A_2} = 10000{\left( {1 + \dfrac{4}{{100}}} \right)^2}$

${A_2} = 10816$ .

The total amount calculated for the 2 years is given by the average of ${A_1}$ and ${A_2}$.

Hence, the $Amount = \dfrac{{{A_1} + {A_2}}}{2}$ $ = (\dfrac{{10609 + 10816}}{2})$ $ = 10712$

$Amount = P\left( {1 + \dfrac{{{R_1}}}{{100}}} \right)\left( {1 + \dfrac{{{R_2}}}{{100}}} \right)\left( {1 + \dfrac{{{R_3}}}{{100}}} \right).........\left( {1 + \dfrac{{{R_n}}}{{100}}} \right)$

The student should be careful in using the formula as many students get confused and simply add the rate of interest ie. $3 + 4 = 7\% $ to get the combined rate of interest which is entirely a wrong approach.

So ,by substituting all the values in equation $\left( 3 \right)$, we get

$Amount = 10000 \times \left( {1 + \dfrac{3}{{100}}} \right)\left( {1 + \dfrac{4}{{100}}} \right) = 10712.$