প্রশ্নে বলা হচ্ছে, ৪% হার সুদে কোনো আসলের 2 বছরে সরল সুদ ও বাৎসরিক চক্রবৃদ্ধি সুদের পার্থক্য 12.80 টাকা হলে আসল কত?

Let, the principal be Tk. x

∴ Amount of compound interest

$$\begin{gathered} = x {\left(1 + \frac{8}{100}\right)}^2 -x \\ = x {\left(\frac{100 + 8}{100}\right)}^2 \\ = x {\left(\frac{108}{100}\right)}^2 -x \\ = x {\left(\frac{27}{25}\right)}^2 -x \\ = x \times \frac{729}{625} -x =\frac{729x}{625} -x = \frac{729x-625x}{625} = \frac{104x}{625}Tk. \end{gathered}$$

And amount of simple interest $= \left(x \times 2 \times \frac{8}{100}\right) =\frac{4x}{25}Tk.$ 

According to the question, $\frac{104x}{625} - \frac{4x}{25} = 12.80$

$$\begin{gathered} \Rightarrow \frac{104x - 100x}{625} = 12.80 \\ \Rightarrow 4x = 625 \times 12.80 \\ \Rightarrow x = \frac{625 \times 12.80}{4} = 625 \times 3.20 \\ \therefore x = 2, 000 Tk. \\ Principal amount is Tk. 2,000 \left(answer\right) \end{gathered}$$