At what rate percent per annum will a sum of Rs. 2000 amounts to Rs. 3125 in 2 years, compounded annually?

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**SOLUTION :**

Here $A=$ Rs. 3125

$\begin{aligned} P &=\text { Rs. } 2000 \\ t &=2 \text { years, } R=? \end{aligned}$

Then, $\left(1+\frac{R}{100}\right)^{t}=\frac{A}{P}$

$\Rightarrow\left(1+\frac{R}{100}\right)^{2}=\frac{3125}{2000}=\frac{625}{400}$

$=\left(\frac{25}{20}\right)^{2}$

$\Rightarrow 1+\frac{R}{100}=\frac{25}{20}$

$\Rightarrow \frac{R}{100}=\frac{25}{20}-1=\frac{5}{20}$

$\therefore R=\frac{5}{20} \times 100$

$=25 \% ;$ Ans.

Therefore, The Rate is 25%.

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