How long will it take for a sum of Rs. 12600 invested at 9% per annum simple interest to amount to Rs. 16002?

Answer

To solve the problem step by step, we will follow the process outlined in the video transcript.

### Step 1: Identify the given values
- Principal (P) = Rs. 12,600
- Rate of interest (R) = 9% per annum
- Amount (A) = Rs. 16,002

### Step 2: Calculate the Simple Interest (SI)
We use the formula for the amount:
\[ A = P + SI \]
Rearranging this gives us:
\[ SI = A - P \]
Substituting the known values:
\[ SI = 16,002 - 12,600 \]
Calculating this gives:
\[ SI = 3,402 \]

### Step 3: Use the Simple Interest formula to find time (T)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
We need to find T, so we rearrange the formula:
\[ T = \frac{SI \times 100}{P \times R} \]
Substituting the known values:
\[ T = \frac{3,402 \times 100}{12,600 \times 9} \]

### Step 4: Simplify the equation
Calculating the denominator:
\[ 12,600 \times 9 = 113,400 \]
Now substituting this back into the equation for T:
\[ T = \frac{3,402 \times 100}{113,400} \]

### Step 5: Calculate T
Now we can simplify:
\[ T = \frac{340,200}{113,400} \]
Dividing gives:
\[ T = 3 \]

### Conclusion
The time it will take for the sum of Rs. 12,600 invested at 9% per annum simple interest to amount to Rs. 16,002 is **3 years**.

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