The difference between a simple interest and annually compounded interest of a principal of 2 years at 8% interest reate is Tk. 12.80. What is the principal amount?

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

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

$= x {(1 + \frac{8}{100})}^{2} - x = x {(\frac{100 + 8}{100})}^{2} = x {(\frac{108}{100})}^{2} - x = x {(\frac{27}{25})}^{2} - x = x \times \frac{729}{625} - x = \frac{729 x}{625} - x = \frac{729 x - 625 x}{625} = \frac{104 x}{625} T k .$

Simple interest এর ক্ষেত্রে,

Total Interest = $I = \frac{p \times r \times t}{100}$

Compound interest এর ক্ষেত্রে,

Compound Amount $= P {(1 + \frac{r}{100})}^{t}$

এখানে, P = আসল; r = সুদের হার; t= সময়

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

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

$\Rightarrow \frac{104 x - 100 x}{625} = 12.80 \Rightarrow 4 x = 625 \times 12.80 \Rightarrow x = \frac{625 \times 12.80}{4} = 625 \times 3.20 ∴ x = 2, 000 T k . P r i n c i p a l a m o u n t i s T k . 2, 000 (a n s w e r)$