CI/Population growth is not a separate theory by itself but mere an extension of Percentage calculation theory. Hence following three questions can be solved with one and same approach, without having to mugup three separate formulas

- A city has 10,000 residents. Its population grows at the rate of 10% per annum, what’ll be its total population after 5 years?
- A bank offers 10% interest rate compounded annually, if you deposit Rs. 10,000 today, what’ll be the total amount in your savings account after 5 years?
- A butler steals 10 ml of whiskey from 100 ml bottle and replaces it with water. He repeats this process 5 more times, how much % whisky is left in the bottle?

**CASE I : CITY POPULATION**

A city has 10,000 residents. Its population grows at the rate of 10% per annum, what’ll be its total population after 5 years?

10% increase

=100% we have already + 10% new is added

=100%+10%

=110%

But if we talk in fraction form: 100% = 1 and 10%=1/10

Hence

10% increase

=1+1/10

=11/10

**AFTER Ist YEAR:**

The new population after 1 year, will be 11/10 times the original

=(11/10)*original ; we know that originally there are 10,000 resident. But no need to calculate that right now.

This is our new original:

**AFTER IInd YEAR:**

The new population will be 11/10 times the original population at the end of first year

=11/10*[(11/10)*original]

**AFTER IIIrd YEAR:**

The new population will be 11/10 times the original

=11/10 [11/10 [(11/10)*original]]

Continuing like this, what we get after 5 years is

**CASE: POPULATION DECLINE**

A city has 10,000 residents. Its population

**declines**at the rate of 10% per annum, what’ll be its total population after 5 years?

Decline = decrease

=100%-10%

=1-(1/10)

=9/10

REPEAT This Step 4 more times.

**EASY WAY :**

**COMPOUND INTEREST IS COMPOUNDED EVERY TIME. i.e YOUR INTEREST INCREASES WITH TIME IT IS VARIABLE IN NATURE WHEREAS SIMPLE INTEREST REMAINS SAME IT IS INVARIABLE. LET US HAVE A LOOK AT SIMPLE INTEREST.**

SIMPLE INTEREST = (P*R*T)/100.

EXAMPLE:

QUESTION 1 - Steve invested Rs. 10,000 in a savings bank account that earned 2% simple interest. Find the interest earned if the amount was kept in the bank for 4 years.

**Solution:**

Principle P = Rs 10,000 Time Period T =4 years and Rate of Interest = 2% = 0.02

Plugging these values in the simple Interest formula,

I = PX T X R {here we have take R in terms of fraction so no need of dividing by 100.

= 10,000 X 4 x 0.02

= Rs. 800

**Interest earned for the investment = Rs. 800.**

QUESTION 2- Ryan bought Rs.15,000 from a bank to buy a car at 10% simple Interest. If he paid Rs. 9,000 as interest while clearing the loan, find the time for which the loan was given.

**Solution :**Principle = Rs 15,000 Rate of Interest R = 10% and the Interest paid = I = Rs. 9,000. And T is to be found.

T = (I x 100) /(PR)

= 9000/(15,000 x 0.10)

= 6 years.

**The loan was given for 6 years.**

So from the above 2 example we just learn about what exactly the SI is Now let us have a simplified Formula for COMPOUND INTEREST.

**AMOUNT = P*(1+R/100)**

^{t}

In This Formula we are having Amount not interest, For calculation of Interest,

INTEREST = AMOUNT - PRINCIPAL.

IN THE ABOVE FORMULA,

P = PRINCIPAL,

R = RATE OF INTEREST IN% per annum,

t = time period,

Now let us try to solve the Above Stated Problems,

Q.A city has 10,000 residents. Its population grows at the rate of 10% per annum, what’ll be its total population after 5 years?

A. In this case P= 10,000

R=10% per annum,

t= 5 years,

using the formula,

Population after 5 years = 10000(1+10/100)

^{5}.

When In some questions there is an increase for 1st year and then there is decrease,In that case

A=P(1+r/100)(1-a/100)......... and so on,

Here in the above formula,

P= Principal/Initial Population,

r= Rate of increase in %,

a= Rate of Decrease in %,

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