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.

Shohan

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2025-01-04 04:42

1 Answers

Shohan

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

$L e t, i n t e r e s t r a t e b e T k . x ∴ C o m p o u n d e d i n t e r e s t = 50, 000 {(1 + \frac{x}{100})}^{2} - 50, 000 S i m p l e i n t e r e s t = \frac{50000 \times x \times 2}{100} A c c o r d i n g t o q u e s t i o n, 50, 000 {(1 + \frac{x}{100})}^{2} - 50, 000 - \frac{50000 \times x \times 2}{100} = 720 \Rightarrow 50, 000 {(1 + \frac{x}{100})}^{2} - \frac{100000 x}{100} = 50, 720 \Rightarrow 50, 000 \frac{(100 + x^{2})}{10000} - 1, 000 x = 50, 720 \Rightarrow 5 {(100 + x)}^{2} - 1, 000 x = 50, 720 \Rightarrow 5 (10, 000 + 200 x + x^{2}) - 1, 000 x = 50, 720 \Rightarrow 50, 000 + + 1, 000 x + 5 x^{2} - 1, 000 x = 50, 720 \Rightarrow 5 x^{2} = 720 \Rightarrow x^{2} = \frac{720}{5} = 144 ∴ x = {(\sqrt{12})}^{2} x = 12$

Answer: Required interest rate is 12%

15 views Answered 2024-12-14 13:31

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