The population of UP increases very rapidly @12% p.a. and 3 years ago its population was 1 million . What is present population ?

Answer

To find the present population of UP given that it increases at a rate of 12% per annum and that its population was 1 million three years ago, we can use the formula for compound interest. The formula for calculating the future value (FV) with compound interest is:

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

Where:
- \( P \) = principal amount (initial population)
- \( r \) = rate of increase (as a decimal)
- \( n \) = number of years

### Step-by-Step Solution:

1. **Identify the values:**
- Initial population \( P = 1,000,000 \)
- Rate of increase \( r = 12\% = 0.12 \)
- Number of years \( n = 3 \)

2. **Substitute the values into the formula:**
\[ FV = 1,000,000 \times (1 + 0.12)^3 \]

3. **Calculate \( (1 + 0.12) \):**
\[ 1 + 0.12 = 1.12 \]

4. **Raise \( 1.12 \) to the power of 3:**
\[ 1.12^3 = 1.12 \times 1.12 \times 1.12 \]
- First, calculate \( 1.12 \times 1.12 = 1.2544 \)
- Then, calculate \( 1.2544 \times 1.12 = 1.407328 \)

5. **Multiply by the initial population:**
\[ FV = 1,000,000 \times 1.407328 = 1,407,328 \]

6. **Conclusion:**
The present population of UP is approximately **1,407,328**.