Question

On a certain sum of money, invested at the rate of 5% per annum compounded annually, the difference between the interest of the first year and the interest of the third year is Rs. 61.50. Find the sum.

• A. Rs. 8000
  
• B. Rs. 11000
  
• C. Rs. 12000
  
• D. None of these
  

Answer 1

Answer: (C)

Rs. 12000

Let the sum (Principle) = Rs. 100
C.I. of 1st year = Rs. \frac{100\times 5\times 1}{100} = Rs. 5$
And, amount of 1st year = Rs. 100 + Rs. 5=Rs. 105$
$\Rightarrow$ The principke for 2nd year = Rs. 105
C.I. of 2nd year $=Rs.\frac{105\times 5\times 1}{100}=Rs.5.25$
And, amount of 2nd year $=Rs.105+Rs.5.25=Rs.110.25$
$\Rightarrow$ The principle for 3rd year $=Rs.110.25$
C.I. of 3rd year $=Rs.\frac{110\times 5\times 1}{100}=Rs.5.5125$
Difference between C.L of 1st year and C.L of 3rd year $=Rs.5.5125-Rs.5=Rs.0.5125$
Now, when the difference of interest $=Rs.0.5125,sum=Rs.100$
And, when the difference of interest $=Rs.61.50,sum=Rs.\frac{100}{0.5125}\times 61.50=Rs.12,000$ (Ans)