# Compound Interest and Formula

In compound interest, the interest for each period is added to the principle before interest is calculated for the next period. With this method the principle grows as the interest is added to it. This method is mostly used in investments such as savings account and bonds.

*Understanding the concept of Compound Interest, Compound Interest formula for exams, shortcut formula of exams, Compound interest and shortcut methods, important tricks for compound interest/simple interest for bank/IBPS/SSC/Railway and other exams, compound interest problems.*

1) A = P + CI | 2) CI = A – P |

3) A = P*(1 + r/100)t | 4) CI = P*[(1 + r/100)t – 1] |

5) If a certain sum of money becomes n times in t years then

Time taken to be

Time taken to be

**na times = a*t.**
To understand compound interest clearly, let’s take an example.

1000 is borrowed for three years at 10% compound interest. What is the total amount after three years?

You can understand the process of compound interest by image shown below.

Year | Principle | Interest (10%) | Amount |

1st | 1000 | 100 | 1100 |

2nd | 1100 | 110 | 1210 |

3rd | 1210 | 121 | 1331 |

**Difference between Simple Interest and compound interest**

After three years,

In simple interest, the total amount would be 1300

And in compound interest, the total amount would be 1331.

**Some Basic Formulas**

If A = Amount

P = Principle

C.I. = Compound Interest

T = Time in years

R = Interest Rate Per Year

**Shortcut Formulas**

**Rule 1:**If rate of interest is R1% for first year, R2% for second year and R3% for third year, then

**Rule 2:**

If principle = P, Rate = R% and Time = T years then

**If the interest is compounded annually:****If the interest is compounded half yearly (two times in year):****If the interest is compounded quarterly (four times in year):**

**Rule 3: If difference between Simple Interest and Compound Interest is given.**

- If the difference between Simple Interest and Compound Interest on a certain sum of money for 2 years at R% rate is given then

- If the difference between Simple Interest and Compound Interest on a certain sum of money for 3 years at R% is given then

**Rule 3:**If sum A becomes B in T1 years at compound interest, then after T2 years

Look up Table

**Find Compound Interest Tricks**

In case of Compound Interest the interest is vary according to time but the first year it is equal that is 1st year Interest is

**Compound Interest = Simple Interest.**

But after that year it is increases. So we can find Compound interest using tricks. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some

more example for your better practice.

more example for your better practice.

**Here is principal is given rate percent and Time is given and find the Compound interest.**

**Example 1:**

Principle is

**15000**at rate percent

**4% p.c.p.a**for

**2 years,**and compound annually

**Find the C.I.**

**Answer:**

We apply the formula to obtain C.I that is

**C.I = p [(1 + r / 100)n – 1]**

**P = 15000.**

**R = 4%.**

**Time = 2 years.**

= 15000 x [( 1 + 4 / 100)2 – 1].

= 15000 x [26×26/25×25 – 1]. [ as we put down (26 / 25)2]

= 15000 x 51 / 625 .

**= 1224**

**Example 2:**

The

**Simple Interest**accrued on an

**amount of Rs.22,500**at the end of 3 years is

**Rs. 10800**what would be the

**Compound Interest accrued**on the

**same amount**at the

**same rate**at the

**end of two years ?**

**Answer :**

Here is given

**amount = 22,500**,

**Time = Years 3**and

**S.I = 10800**so we need to find Rate percent.

**Step 1:**we know S.I = P x R x T / 100

10,800 = 22,500 x R x 3 / 100

R = 1080000 / 67500 = 16 % So R = 16 %.

**Step 2:**Compound Interest accrued on the

**same amount**at the

**same rate**at the

**end of two years**

is we apply the formula

C.I = 22500 x (116 / 100 x 116 / 100 – 1 )

= 22500 x( 116 x 116/ 10000 – 1) = 22500 x( 13456 / 1000) – 1 = 22500 x (1.3456 – 1) = 22500 x 0.3456 =7776

So the C.I end of two years is 7776.

**Example 3:**

What will be the compound interest on a sum of Rs.4800/- at the rate of 6 p.c.p.a for 2 years ?

**Answer:**

Compound Interest = P[1+R/100]n-1

4800[( 1 + 6 / 100 )2 – 1]

4800 [53 x 53 / 50 x 50 – 1 ]

=593.28

So the compound interest is 593.28

**Example 4:**

What would be the compound interest obtained on an amount of Rs.1,600 at the rate of 8 p.c.p.a after two years ?

**Answer:**

Amount = SI + Principle

compound Interest = p ( 1 + r / 100)n – 1600

1600 ( 1 + 8 / 100 )2 – 1600

( 1600 x 27 x 27 / 25 x 25 ) – 1600

= ( 1866.24 – 1600 )

= 266.24

**Example 5:**

What would be the compound interest obtained on an amount of Rs. 6000 at the rate of 10% p.a . after 2 years ?

**Answer :**

6000[ (1 + 10 / 100) ]n-1

= 6000 [ (11 / 10 )2 – 1]

= 6000 x 21 / 100

= 1260

So the compound interest is 1260.

**Example 6:**

What would be the compound interest obtained on an amount of Rs.8850 at the rate of 12 p.c.p.a after two years?

**Answer :**

Amount = 8850

rate = 12

Time = 2 years

compound interest = ?

A = 8850 ( 1 + 12 / 100 )2

= 8850 x 28 x 28 / 25 x 25

= 11101.44

So Amount = Rs.11101.44

C.I = ( 8850 – 11101.44 ) = 2251.44

### Find The rate % based question

Now we try to put all types of shortcut tricks on rate % based. But it possible we miss any. We appreciate if you share that with us. Your help will help others.

When we borrowed money from some one or we lent out some money for a some certain period is called the Principle or Sum. So here we, Find the Rate % based questions are given in bank exams and Time will be given.

just using formula u get rate percent. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some more example for your better practice.

What is the rate of p.c.p.a ? If the simple interest accrued on amount of Rs.25500 at the end of 3 years is 9180.

we know the formula is S.I = PRT / 100

So, S.I = 9180 , P = 25500 , T = 3 years , R = ?

9180 = 25500 x R x 3 / 100

R = 9180 / 765 = 12 %

So rate of p.c.p.a = 12 %

just using formula u get rate percent. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some more example for your better practice.

**Example 1:**What is the rate of p.c.p.a ? If the simple interest accrued on amount of Rs.25500 at the end of 3 years is 9180.

**Answer :**we know the formula is S.I = PRT / 100

So, S.I = 9180 , P = 25500 , T = 3 years , R = ?

9180 = 25500 x R x 3 / 100

R = 9180 / 765 = 12 %

So rate of p.c.p.a = 12 %

**Example 2:**

At what rate percent annul will a sum of money double in a 4 years.

**Answer :**

Let Principle is = P.Then S.I = P and Time = 4 years.

S.I. = ( PRT/100 ).

So, R = ( 100X P / P X T ) %.

R = 25%

**Similarly we learn another example:**

**Example 3:**

A sum of money is in double in 12 years At what rate percent per annul.

**Answer :**

Let Principle = P. Then S.I = P and T is given 12 years.

Rate = ( 100 X P / P X 12 ) = 8.33%

So R = 8.33 %

**Example 4:**

If the Simple interest accrued in 8 years on a principal of Rs.40,000/- is 8000 of the principal.What is the rate of simple interest p.c.p.a?

**Answer :**

SI = PRT / 100

Let the rate of simple interest is x

So

x = 100 x 8000 / 40000 x 8

x = 2.5

So the rate of simple interest is 2.5.

## Population based Compound Interest

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

=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 first 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:

This is our new original:

**After second year**

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

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

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

**After third year**

The new population will be 11/10 times the original

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

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

Continuing like

this, what we get after 5 years is

this, what we get after 5 years is

####
**CASE: City’s**

Population: Decline

Population: Decline

A city has 10,000 residents. Its population

what’ll be its total population after 5 years?

Decline = decrease

=100%-10%

=1-(1/10)

=9/10

**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

**Population after 5 years**

Answer. After 5 years, city’s population will be 5904.

**PRACTICE**

**Example 1:**

The compound interest on a certain sum at a certain rate of interest for the 2nd year is Rs. 2,200 and for the 3rd year is Rs. 2,420. Find the principal and rate of interest.

**Example 2:**Rs.25,000 is invested for 3 years at 12% compound interest p.a. What is the interest in the third year?

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