The population of a town is 352800.If it increases at the rate of 5% per annum,then what will be its population 2 yr hence. Also, find the population 2 yr ago.

Answer

To solve the problem, we will calculate the population of the town after 2 years with a 5% annual increase and also find the population 2 years ago.

### Step 1: Calculate the population after 2 years with a 5% annual increase.

1. **Identify the initial population and the rate of increase:**
- Initial population (P) = 352,800
- Rate of increase (r) = 5% = 0.05

2. **Use the formula for compound interest to find the population after 2 years:**
\[ P_{future} = P \times (1 + r)^n \]
where \( n \) is the number of years.

3. **Substituting the values into the formula:**
\[ P_{future} = 352800 \times (1 + 0.05)^2 \]
\[ P_{future} = 352800 \times (1.05)^2 \]
\[ P_{future} = 352800 \times 1.1025 \]
\[ P_{future} = 388962 \]

### Step 2: Calculate the population 2 years ago.

1. **To find the population 2 years ago, we will use the formula for population decrease:**
\[ P_{past} = \frac{P_{future}}{(1 + r)^n} \]

2. **Substituting the future population and the rate of increase:**
\[ P_{past} = \frac{352800}{(1 + 0.05)^2} \]
\[ P_{past} = \frac{352800}{(1.05)^2} \]
\[ P_{past} = \frac{352800}{1.1025} \]
\[ P_{past} = 320000 \]

### Final Answers:
- The population 2 years hence will be **388,962**.
- The population 2 years ago was **320,000**.

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