Answer

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**Hint**: The problem can be solved easily with the concept of simple interest. Interest is the amount of money gained on the principal over a certain period of time.

**:**

__Complete step-by-step answer__In the given problem,

Principal $ = P = Rs\,6,000 $

Rate of interest $ = R $ $ \% $

Time Duration $ = 1\,year\,\,6\,months\, $

Converting the time duration in years only, we get,

Time Duration $ = 1.5\,year $

Since we know that a year consists of twelve months.

Now, the amount paid by Alok to clear the debt is given to us as $ Rs\,6720 $ . Hence, the final amount paid is $ Rs\,6720 $ .

Now, we get the simple interest as $ Interest = Amount - principal $ . So, we have the Simple interest as $ Rs6720 - Rs6000 = Rs720 $ .

Now, we know the formula for the calculation of simple interest as

$ Interest = \dfrac{{P \times R \times T}}{{100}} $ .

So, substituting the values of the known quantities, we get,

$ \Rightarrow Rs720 = \dfrac{{Rs6000 \times R \times 1.5}}{{100}} $

Now, we need to calculate the value of rate of interest using the equation above. So, isolating the only unknown quantity in the equation R, we get,

\[ \Rightarrow \dfrac{{720 \times 100}}{{6000 \times 1.5}} = R\]

Carrying out the calculations and finding the value of R, we get,

\[ \Rightarrow R = \dfrac{{72000}}{{9000}}\]

Cancelling the common factors in numerator and denominator, we get,

\[ \Rightarrow R = 8\]

So, the rate of interest charged by the bank is $ 8\% $ .

**So, the correct answer is “$ 8\% $”.**

**Note**: Simple interest is very easy to calculate when we are given the principal amount, the time duration for which the loan is taken and the rate of interest charged by the institution which in this case is the bank. We must take care of the calculations to be sure of the final answer.

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