In our Day-Day Lives, we see entities such as Population of a City, Value of a Property, Weight of a Child, Height of a Tree that grow over a period of time. We call the Increase in Quantity as Growth and the Growth Per Unit Time is known as the Rate of Growth. If the Growth Rate occurs at the Same Rate then we call it Uniform Increase or Uniform Growth Rate. Check the Formulas for Uniform Rate of Growth and the Solved Problems for finding the Principal of Compound Interest in Uniform Rate of Growth explained step by step.

## How to find the Uniform Rate of Growth?

Learn how to calculate the uniform growth rate by referring to the below modules.

If the Present Value P of a quantity increases at the rate of r % per unit of time then the value Q of the quantity after n units of time is as such

Q = P(1+r/100)^{n}

Growth is obtained by subtracting the Increased Value from the Actual Value

Growth = Q – P

= P(1+r/100)^{n} – P

= P{(1+r/100)^{n} -1}

### Solved Examples on Principal of Compound Interest in Uniform Rate of Growth

1. The population of the town increases by 8% every year. If the present population is 7000, what will be the population of the town after 2 years?

Solution:

Given Current Population = 7000

n = 2 Years

Rate of Interest = 8%

Q = P(1+r/100)^{n}

Substitute the input values in the above formula

= 7000(1+8/100)^{2}

= 7000(1+0.08)^{2}

= 7000(1.08)^{2}

= 7000(1.1664)

= 8164

Population of a Town after 2 years is 8164.

2. John buys a plot of land for $ 20,000. If the value of the land appreciates by 10% every year then find the profit that John will make by selling the plot after 3 years?

Solution:

P = $20,000

interest rate = 10%

n = 3 years

Q = P(1+r/100)^{n}

= 20,000(1+10/100)^{3}

= 20,000(1+0.1)^{3}

= 20,000(1.1)^{3}

= $26620

Profit made by John = $26620 – $20,000

= $6,620

3. Mike purchased a bike for Rs. 45,000. If the cost of his bike is appreciated at a rate of 5% per annum, then find the cost of the bike after 3 years?

Solution:

Initial Price = Rs. 45, 000

Rate of Appreciation = 5 % Per Annum

n = 3 years

Q = P(1+r/100)^{n}

= 45,000(1+5/100)^{3}

= 45,000(1+0.05)^{3}

= 45,000(1.05)^{3}

= Rs. 52093

Therefore, the Cost of the Bike after 3 years is Rs. 52093.

Read More: