The population of a village increases at a rate of 5% every year. If the present population of the village is 5620, find the population after 1 year.

Options

A. 5805
B. 6121
C. 5901
D. 6000

Explanation

To find the population of the village after one year, we will use the formula for calculating the amount after a percentage increase. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Present population (Principal) = 5620
- Rate of increase = 5%
- Time period (n) = 1 year

### Step 2: Write the formula for population after one year
The formula to calculate the population after one year with a percentage increase is:
\[ \text{Population after 1 year} = \text{Principal} \times \left(1 + \frac{\text{Rate}}{100}\right)^n \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ \text{Population after 1 year} = 5620 \times \left(1 + \frac{5}{100}\right)^1 \]

### Step 4: Simplify the expression
First, calculate \(1 + \frac{5}{100}\):
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]

Now substitute this back into the equation:
\[ \text{Population after 1 year} = 5620 \times 1.05 \]

### Step 5: Calculate the final population
Now, multiply:
\[ \text{Population after 1 year} = 5620 \times 1.05 = 5910 \]

### Final Answer
The population of the village after one year will be **5910**.

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