Question

Govind borrows Rs. 18,000 at 10% simple interest. He immediately invests the money borrowed at 10% compound interest compounded half-yearly. How much money does Govind gain in one year?

• A. Rs. 80
  
• B. Rs .50
  
• C. Rs. 45
  
• D. Rs. 25
  

Answer 1

Answer: (C)

Rs. 45

Sum=Rs.18000

Rate =10%

Time =1 year

$S.I=\frac{PRT}{100}$

$\Rightarrow \frac{18000\times 10\times 1}{100}=Rs.1800$

Govind invest the sum at 10% compound interest half-yearly

Then amount after 1 year

R=10% half-yearly=$\frac{10}{2}=5$%

Time =1 year=2 half year

$amount=P{(1+\frac{R}{100})}^T$

$\Rightarrow 18000{(1+\frac{5}{100})}^2$

$\Rightarrow 18000\times \frac{105}{100}\times \frac{105}{100}$

$\Rightarrow Rs.19845$

$C.I=amount-Sum$

$=19845-18000=Rs.1845$

Difference between C.I and S.I$=1845-1800=Rs.45$

Hence Govind gain Rs.45 in a year