Lesson SIMPLE INTEREST VERSUS COMPOUND INTEREST

Source code of 'SIMPLE INTEREST VERSUS COMPOUND INTEREST'

This Lesson (SIMPLE INTEREST VERSUS COMPOUND INTEREST) was created by by Theo(13342)

Here�s some information from the web on simple interest versus compound interest.

<a href = "http://www.basic-mathematics.com/simple-vs-compound-interest.html" target = "_ blank">http://www.basic-mathematics.com/simple-vs-compound-interest.html</a>

The difference between Simple Interest calculations and Compound Interest calculations is this:

Simple Interest is calculated from the principal only (the amount that you deposited).
Compound Interest is calculated from the remaining balance (this includes the principal plus any interest that you earned that still remains in the account).

A very simple example shows the difference:

Assume you put $5,000 in the bank.
Assume the interest rate is 3.75% per year.
Assume you withdraw the money at the end of 3 years.

With simple interest, the interest each year is calculated from the principal you put in the bank which is $5,000.  The interest that you already earned is not used in the calculation.

With compound interest, the interest each year is calculated from the remaining balance.  This includes your principal plus any interest that you previously earned that still remains in the account.

The associated picture of an excel printout shows an example of $5,000 put in an account for 3 years.

It shows what the account will look like using simple interest and it shows what the account will look like with compound interest.

With simple interest, the interest is calculated from $5,000 each year.
That is the amount that you put in the bank (the principal).
You can see that in the Simple Interest Table.

With compound interest, the interest is calculated from the remaining balance.
This includes the amount that you put in the bank (the principal) plus any interest that you already earned on that principal (accrued interest).
You can see that in the Compound Interest Table.
The description of what happens in that Compound Interest Table is shown below:

In year 1, it�s calculated from $5,000.  
This is the initial amount deposited in the account.
In year 2, it�s calculated from $5,187.5
This is the initial amount deposited in the account plus the interest earned during the first year.
In year 3, it�s calculated from $5,382.03
This is the balance from year 2 plus the interest earned on that balance during the year.
In year 4, it�s calculated from $5,583.86
This is the balance from year 3 plus the interest earned on that balance during the year.

See the picture below which shows an Excel File and the calculations that were performed in it.

In the Simple Interest Table on the left, you can see that the interest calculated each year (column I) is based on the principal that was invested (column P).  
Interest is not calculated on the Remaining Balance.

In the Compound Interest Table on the right, you can see that the interest calculated each year (column I) is based on the Remaining Balance (column B1).  The Remaining Balance contains the Principal plus any interest that was previously earned.

That's the main difference.
The formulas take this into account.

The formula for Balance in the account using Simple Interest is:
B = P + P*R*T
This can also be shown as:
B = P*(1 + R*T)

The formula for Balance in the account using Compound Interest is:
B = P * (1+R)^T

B is the balance
P is the principal
R is the interest rate
T is the time

Interest Rate and Time are synchronized with each other.
If R is per year, than T is number of years.
If R is per month, then T is number of months.