Question

Vikram borrowed Rs. $2000$ from a bank at $10\%$ per annum simple interest. He lent it to his friend Venkat at the same rate but compounded annually. Find his gain after $2\frac{1}{2}$ years.

• A. $280$
• B. $38.117$
• C. $370$
• D. $347.13$

Answer 1

The correct option is B $38.117$

Principal , $P=Rs.2000$

Rate of interest of bank , $r=10$%

Time, $t=2\frac{1}{2}=\frac{5}{2}$ years

Simple interest $=\frac{P\times r\times t}{100}$

$=\frac{2000\times 10\times 5}{100\times 2}$$=500$

So, Vikram has to pay $2000+500=Rs.2500$ to the bank, after $2.5$ years.

Vikram lent Rs. $2000$ to Venkat at same rate compounded annually.

So, the Amount Vikram will get from Venkat after $2.5$ years $=P{(1+\frac{r}{100})}^t$

$=2000{(1+\frac{10}{100})}^{2.5}$

$=2000{\left(\frac{11}{10}\right)}^{2.5}$

$=2000\times \frac{11}{10}\times \frac{11}{10}\times \sqrt{\frac{11}{10}}$

$=2420\sqrt{1.1}$

$=2538.117$

So, Vikram's gain $=2538.117-2500=Rs.38.117$