Answer

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**Hint:**Since three different rate of interests are given for the three years respectively, so we will use the formula for Amount as:

\[A = P\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right)\left( {1 + \dfrac{{{r_3}}}{{100}}} \right)\]

And Interest will be the difference between Amount and Principal.

**Complete step-by-step solution:**

Now, according to the statement of the question, the Principal given is 17000, time is of 3years and the rate of interest for three years is 10% for first year, 10% for second year and 14% for third year.

So now according to the formula, the Amount is given as:

\[A = P\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right)\left( {1 + \dfrac{{{r_3}}}{{100}}} \right)\]

And the Interest will be calculated as: Interest = Amount – Principal

Now, first we will calculate the Amount as per the information in the question, using the formula given above:

So,

$

P = Rs.15000 \\

{r_1} = 6\% ,{r_2} = 8\% ,{r_3} = 10\% \\

t = 3years \\

$

Then the amount will be:

$

A = 15000\left( {1 + \dfrac{6}{{100}}} \right)\left( {1 + \dfrac{8}{{100}}} \right)\left( {1 + \dfrac{{10}}{{100}}} \right) \\

= 15000\left( {\dfrac{{100 + 6}}{{100}}} \right)\left( {\dfrac{{100 + 8}}{{100}}} \right)\left( {\dfrac{{100 + 10}}{{100}}} \right) \\

= 15000\left( {\dfrac{{106}}{{100}}} \right)\left( {\dfrac{{108}}{{100}}} \right)\left( {\dfrac{{110}}{{100}}} \right) \\

= \dfrac{{15 \times 106 \times 108 \times 11}}{{100}} \\

= 18889.20 \\

$

Therefore, the Amount is ₹18889.20

$

Interest = Amount - Principal \\

= 18889.20 - 15000 \\

= 3889.20 \\

$

So, after 3 years the total amount earned is ₹18889.20 while the total interest earned is ₹3889.20

Therefore, the total interest earned in 3 years is ₹3889.20

**Hence, the correct answer is option B.**

**Note:**To calculate the interest earned we need to calculate the amount first. If there are n different rate of interests for n years, then, the formula for Amount will become:

\[A = P\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right)\left( {1 + \dfrac{{{r_3}}}{{100}}} \right).........\left( {1 + \dfrac{{{r_n}}}{{100}}} \right)\]

However, the Interest will always be calculated as the difference of Amount and Principal.. This is accumulated interest , compounded over n years. Hence called Compound Interest with variable rate of interests.

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