Question

The difference between the compound and simple interest on a sum of money for $2$ years at $6\frac{1}{4}$% per annum is Rs. $10$. The sum is

• A. $2000$
• B. $2560$
• C. $2500$
• D. $2600$

Answer 1

The correct option is B $2560$

Compound interest, $A_c=P\times {(1+\frac{r}{100n})}^{nt}$

Where , $P$ is the principle

$r$ is the rate $\left(in\%\right)$

$n$ is the compound number

$t$ is time

and similarly

simple interest, $A_s=\frac{P\times r\times t}{100}+P$

So, According to the question,

$|A_s-A_c|=Rs10$

$\Rightarrow |\left(\frac{P\times 25/4\times 2}{100}\right)+R{(1+\frac{25}{4\times 100\times 1})}^{1\times P}\times P|=Rs10$

$\Rightarrow |P+\frac{P}{8}-{(1+\frac{1}{16})}^2|=Rs10$

$\Rightarrow |P+\frac{P}{8}-\left(\frac{(17{)}^2}{{16}^2}\right).P|=Rs10$

$\Rightarrow |\frac{9P}{8}-\frac{{17}^2}{{16}^2}P|=Rs10$

$P|\frac{9}{8}-\frac{289}{256}|=Rs10$

$\Rightarrow P\left|\frac{288-289}{256}\right|=Rs10$

$\Rightarrow \frac{P}{256}=Rs10$

$\Rightarrow P=Rs2560$