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.

Compound Interest Concept

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

Compound Interest Formula

Compound Interest

Shortcut Formulas

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

Compound Interest Shortcut Methods

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%

Compound Interest Shortcut Methods

Compound Interest Shortcuts

Compound Interest Shortcut Formulas

(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:

    Compound Interest

  2. If the interest is compounded half yearly (two times in year):

    Compound Interest Shortcut Formulas

  3. If the interest is compounded quarterly (four times in year):

    Compound Interest Shortcut Methods

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

Compound Interest
Compound Interest Shortcuts
Compound Interest Shortcut Formulas

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

A = 1081.6
If the interest is compounded half yearly

Compound Interest Shortcut Formulas
Compound Interest Shortcut Methods

A = 1082.4
If the interest is compounded quarterly

Compound Interest Shortcut Methods
Compound Interest Shortcuts

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

    Compound Interest Shortcut Formulas

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:

Compound Interest Shortcut Formulas

Compound Interest Shortcuts

 

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

    Compound Interest Shortcuts

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:

Compound Interest Shortcuts

Compound Interest Shortcut Formulas

 

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

Compound Interest Shortcut Methods

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

Compound Interest Shortcuts

 

Look up Table

Compound Interest Look Up Table

 

 

 

 


Our Forum

We are providing a forum where students can post their questions regarding any exams and any subjects. Our subject experts are always there to give answers and being a bright member, you also can give answers to these questions.

Go to Forum »

Like Us On Facebook

Follow Us on Google+