Estimating Population Growth using Compound Interest

To estimate the population of a country in the year 2015, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = final amount (population in 2015)
P = initial amount (population in 2005)
r = annual interest rate (2%)
n = number of times the interest is compounded per year (1)
t = number of years (10)

Using the formula above, we can estimate the population of the country in 2015 as follows:

A = 55 crores(1 + 0.02/1)^(1*10)
A = 55 crores(1 + 0.02)^10
A = 55 crores(1.02)^10
A = 55 crores(1.218994)
A = 66.54 crores

Therefore, the estimated population of the country in 2015 is 66.54 crores.

Explanation of the Formula

The formula for compound interest is used to calculate the growth of an investment over time. In this case, we are using it to estimate the growth of the population of a country. The formula takes into account the initial amount (P), the annual interest rate (r), the number of times the interest is compounded per year (n), and the number of years (t).

In this case, the initial amount is the population of the country in 2005 (55 crores), the annual interest rate is 2%, the number of times the interest is compounded per year is 1, and the number of years is 10 (from 2005 to 2015).

By plugging these values into the formula, we can calculate the final amount (A), which is the estimated population of the country in 2015.

Conclusion

Using the formula for compound interest, we can estimate the population of a country in the future based on its current population and the rate of population growth. This can be useful for planning purposes, such as determining the need for infrastructure, resources, and services in the future.