Find the interest rate of an investment of BDT 50,000 for 2 years where the difference between the amounts of compound interest and simple interest is BDT 720.

প্রশ্নে বলা হচ্ছে 50,000 টাকার 2 বছরের চক্রবৃদ্ধি সরল সুদের পার্থক্য 720 টাকা হলে সুদের হার কত?

$$\begin{gathered} Let, interest rate be Tk. x \\ \therefore Compounded interest = 50,000 {\left(1+\frac{x}{100}\right)}^2-50,000 \\ Simple interest = \frac{50000\times x\times 2}{100} \\ According to question, \\ 50,000 {\left(1+\frac{x}{100}\right)}^2-50,000-\frac{50000\times x\times 2}{100}=720 \\ \Rightarrow 50,000 {\left(1+\frac{x}{100}\right)}^2-\frac{100000x}{100}=50,720 \\ \Rightarrow 50,000\frac{(100+x^2)}{10000}-1,000x=50,720 \\ \Rightarrow 5 {(100+x)}^2-1,000x= 50,720 \\ \Rightarrow 5 (10,000+200x+x^2)-1,000x=50,720 \\ \Rightarrow 50,000++1,000x+5x^2-1,000x=50,720 \\ \Rightarrow 5x^2 = 720 \\ \Rightarrow x^2= \frac{720}{5}=144 \\ \therefore x= {\left(\sqrt{12}\right)}^2 \\ x = 12 \end{gathered}$$

Answer: Required interest rate is 12%