Question

Find the sum of which the difference between the simple interest and the compound interest at the rate of 8% per annum compounded annually be Rs. 64 in 2 years.

• A. Rs. 8,000
• B. Rs. 10,000
  
• C. Rs. 12,000
  
• D. Rs. 15,000
  

Answer 1

Answer: (B)

Rs. 10,000

Let the sum be Rs.P

Time =2year

Rate=8%

S.I for 2 years$=\frac{P\times 8\times 2}{100}=\frac{4P}{25}$

C.I for 2 years$=\left[P{(1+\frac{8}{100})}^2\right]-P$

$\Rightarrow [P\times \frac{108}{100}\times \frac{108}{100}]-P$

$\Rightarrow \frac{729P}{625}-P=\frac{104P}{625}$

According to the question

$\Rightarrow \frac{104P}{625}-\frac{4P}{25}=64$

$\Rightarrow \frac{104P-100P}{625}=64$

$\Rightarrow 4P=64\times 625$

$\Rightarrow P=\frac{64\times 625}{4}=Rs.10000$