Let’s assume that the Annual payment is Rs. M.

Now, the debt of Rs. 38100 is due in 3 years, it means that if all the debt is cleared at once, an amount of Rs. 38100 should be paid after 3 years.

But obviously, while clearing the debt through annual installments, the total amount payable will be less.

Once the first installment is paid, it will be excluded from interest calculation, and interest will be calculated for the remaining amount next year.

After the 2^nd installment, the amount worth 2 installments will be excluded from interest calculations and so on.

Hence, in order to balance the installments and actual amount payable, we write:

$( \Rightarrow M{\left( {1 + \frac{R}{{100}}} \right)^2} + M\left( {1 + \frac{R}{{100}}} \right) + M = A)$

Where, M = annual installment, R = % rate of interest, A = total debt

Here, A = 38100, R = 50/3

$( \Rightarrow M{\left( {1 + \frac{{\frac{{50}}{3}}}{{100}}} \right)^2} + M\left( {1 + \frac{{\frac{{50}}{3}}}{{100}}} \right) + M = 38100)$

$(\begin{array}{l} \Rightarrow M{\left( {1 + \frac{1}{6}} \right)^2} + M\left( {1 + \frac{1}{6}} \right) + M = 38100\\ \Rightarrow \frac{{49M}}{{36}} + \frac{{7M}}{6} + M = 38100\\ \Rightarrow \frac{{127M}}{{36}} = 38100 \end{array})$