Consider an amount ₹ 1000. If this grows at 10% p.a., how long will it take to double when compounding is done vs. when Class 8

Consider an amount ₹ 1000. If this grows at 10% p.a., how long will it take to double when compounding is done vs. when Class 8

Question 1.

Consider an amount ₹ 1000. If this grows at 10% p.a., how long will it take to double when compounding is done vs. when compounding is not done? Is compounding an example of exponential growth and not-compounding an example of linear growth? Class 8

Solution:

With compounding:

Let the amount double in t years.

So, 2000 = 1000[latex]\left(1+\frac{10}{100}\right)^t[/latex]

or 2 = (1 + 0.1)^t

or (1.1)^t = 2.

Now, 1.1 × 1.1 × 1.1 × 1.1 × 1.1 × 1.1 × 1.1 × 1.1 = 2.14.

So, it will double in about 8 years.

Without compounding:

Let it be doubled in t years.

So, from I = prt,

2000 - 1000 = 1000 × [latex]\frac{10}{100}[/latex] × t

or 1000 = [latex]\frac{1000 \times t}{10}[/latex]

or t = 10 years.

Question 2.

The population of a city is rising by about 3% every year. If the current population is 1.5 crore, what is the expected population after 3 years? Class 8

Solution:

Population after 3 years

= 1.5 [latex]\left(1+\frac{3}{100}\right)^3[/latex] crore

= 1.5 × [latex]\frac{103 \times 103 \times 103}{100 \times 100 \times 100}[/latex] crore

= 1.639 crore (approx.)