What will Rs. 5000 amount to in 10 years, compounded annually at 10 % per annume ? `["Given "(1.1)^(10)=2.594]`

Answer

To find the amount that Rs. 5000 will grow to in 10 years when compounded annually at a rate of 10% per annum, we can use the formula for compound interest:

\[ A = P(1 + r)^n \]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.

### Step-by-Step Solution:

1. **Identify the values:**
- Principal amount \( P = 5000 \)
- Annual interest rate \( r = 10\% = 0.10 \)
- Number of years \( n = 10 \)

2. **Substitute the values into the formula:**
\[ A = 5000(1 + 0.10)^{10} \]

3. **Calculate \( 1 + r \):**
\[ 1 + 0.10 = 1.10 \]

4. **Raise \( 1.10 \) to the power of \( 10 \):**
\[ (1.10)^{10} = 2.594 \quad \text{(given)} \]

5. **Substitute back into the formula:**
\[ A = 5000 \times 2.594 \]

6. **Calculate the final amount:**
\[ A = 5000 \times 2.594 = 12970 \]

### Final Answer:
The amount after 10 years will be Rs. 12970.