Question

The sum of money amounts to ₹13,225 in two years at 15% compound interest annually. Find the sum.

• A. ₹10,000
• B. ₹9,500
• C. ₹11,000
• D. ₹10,500

Answer 1

Answer:

A. ₹10,000

To find the sum (principal), we can use the compound interest formula.

Given Data:

• Amount ($A$) = ₹13,225

• Time ($n$) = $2$ years

• Rate of Interest ($R$) = $15\%$ per annum

Step-by-Step Calculation:

1. Write the compound interest formula:

   
   

   $A = P \left(1 + \frac{R}{100}\right)^n$

   Where:

   
   

   • $A$ = Amount

   • $P$ = Principal (Sum)

   • $R$ = Rate of interest

   • $n$ = Time period

2. Substitute the given values into the formula:

   
   

   $13225 = P \left(1 + \frac{15}{100}\right)^2$

3. Simplify the fraction inside the parentheses:

   
   

   $\frac{15}{100} = \frac{3}{20}$

   $1 + \frac{3}{20} = \frac{23}{20}$

   So the equation becomes:

   
   

   $13225 = P \left(\frac{23}{20}\right)^2$

   $13225 = P \times \frac{529}{400}$

4. Solve for P

   
   $P = 13225 \times \frac{400}{529}$

   Since $529 = 23^2$ and $13225 \div 529 = 25$:

   
   

   $P = 25 \times 400$

   $P = 10,000$

Answer:

The sum of money (principal) is ₹10,000.