Population Growth Calculation:

Given:
- Population in 2005 = 55 crore
- Annual growth rate = 2%

To calculate the population in 2015, we need to use the concept of Compound Interest (CI) because the population is growing at a constant rate.

Formula for Compound Interest:
The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)

Where:
A = Final amount
P = Principal amount (initial population)
r = Annual interest rate (growth rate in this case)
n = Number of times that interest is compounded per year
t = Number of years

Calculation:

Step 1: Convert the population from crore to a regular number by multiplying by 100 million.
Initial population in 2005 = 55 crore = 55 * 100 million = 5500 million

Step 2: Calculate the population growth rate in decimal form.
Annual growth rate = 2% = 0.02

Step 3: Calculate the population for 2015 using the compound interest formula.
A = P(1 + r/n)^(nt)
= 5500 million * (1 + 0.02/1)^(1*10)
= 5500 million * (1 + 0.02)^10
= 5500 million * (1.02)^10
≈ 5500 million * 1.2184
≈ 6700 million

Step 4: Convert the population back to crore by dividing by 100 million.
Final population in 2015 = 6700 million / 100 million = 67 crore

Therefore, the estimated population in the year 2015 is 67 crore.