COMPOUND INTEREST

Compound Interest Concept & Shortcut Methods

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.

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

See Example

Find the total amount after three years on Rs 1000 if the compound interest rate for first year is 4%, for second year is 5% and for third year is 10%
Sol:

P = 1000
R₁ = 4%, R₂ = 5% and R₃ = 10%

(From the table given at the bottom of the page)

A = 1201.2

Rule 2:
If principle = P, Rate = R% and Time = T years then

1. If the interest is compounded annually:
   
2. If the interest is compounded half yearly (two times in year):
   
3. If the interest is compounded quarterly (four times in year):
   

Example

Find the total amount on 1000 after 2 years at the rate of 4% if

1. The interest is compounded annually
2. The interest is compounded half yearly
3. The interest is compounded quarterly.

Sol:

Here P = 1000
R = 4%
T = 2 years
If the interest is compounded annually

(From the table given at the bottom of the page)

A = 1081.6
If the interest is compounded half yearly

 A = 1082.4

If the interest is compounded quarterly

A = 1082.9

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
• 
  

Example

If the difference between simple interest and compound interest on a certain sum of money at 10% per annum for 2 years is Rs 2 then find the sum.
Sum:

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

Example

If the difference between simple interest and compound interest on a certain sum of money at 10% per annum for 3 years is Rs 2 then find the sum.
Sol:

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

Example

Rs 1000 becomes 1100 after 4 years at certain compound interest rate. What will be the sum after 8 years?
Sum:
Here A = 1000, B = 1100
T₁ = 4, T₂ = 8

Look up Table: