Raviraj invested an amount of Rs. 10000 at compound interest rate of 10% per annum for a period of three years. How much amount will Raviraj get after 3 years ?

Answer

To find out how much amount Raviraj will get after 3 years from his investment of Rs. 10,000 at a compound interest rate of 10% per annum, we can follow these steps:

### Step 1: Identify the formula for compound interest
The formula to calculate the total amount (A) after t years at compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \( A \) = total amount after time t
- \( P \) = principal amount (initial investment)
- \( r \) = annual interest rate (in percentage)
- \( t \) = time (in years)

### Step 2: Substitute the known values into the formula
Here, the principal amount \( P = 10,000 \), the rate \( r = 10\% \), and the time \( t = 3 \) years. Substituting these values into the formula gives:
\[ A = 10,000 \left(1 + \frac{10}{100}\right)^3 \]

### Step 3: Simplify the expression inside the parentheses
Calculating \( \frac{10}{100} \) gives \( 0.1 \). Therefore:
\[ A = 10,000 \left(1 + 0.1\right)^3 \]
This simplifies to:
\[ A = 10,000 \left(1.1\right)^3 \]

### Step 4: Calculate \( (1.1)^3 \)
Now, we need to calculate \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 \]
Calculating this step-by-step:
- First, \( 1.1 \times 1.1 = 1.21 \)
- Then, \( 1.21 \times 1.1 = 1.331 \)

So, \( (1.1)^3 = 1.331 \).

### Step 5: Multiply by the principal amount
Now, substitute back into the equation for \( A \):
\[ A = 10,000 \times 1.331 \]
Calculating this gives:
\[ A = 13,310 \]

### Conclusion
Thus, the total amount Raviraj will get after 3 years is:
\[ \text{Total Amount} = Rs. 13,310 \]