What is compound interest?

What is compound interest?
We know that if the principle remains the same for the entire period of time then the interest is called the simple interest. However in practice the method according to which banks, insurance corporations and other money lending and deposit taking companies calculate interest is called the compound interest. We can define the compound interest as the interest that accrues when earnings of each specified period of time is added to the principle thus increasing the principle base on which subsequent interest in computed. In other words, when we calculate interest on interest, its called compound interest.

How to calculate compound interest?
That can be explained with the following example:
Suppose $ 50000.00 are deposited in a bank for 2 years at 7% per annum interest compounded annually. What is a Compound Interest? The interest can be calculated in the following way:
Principle amount = P = $ 50000
Rate of interest = r = 7% = 0.07 per dollar per year
Number of years = t = 2
1. Interest for the first year, n = 1
Simple interest = P * r * n
So, I = 50000 * 0.07 * 1 = $ 3500.00
2. Interest for the second year
For calculating the interest for the second year, principle would not be the same as the initial deposit. Principal for the second year = initial deposit + interest for the first year.
Therefore now P = 50000 + 3500 = 53500
So now I = 53500 * 0.07 * 1 = 3745
So total interest for first and second year = 3500 + 3745 = $ 7245
3. If we were asked to find the total interest for 3 years then now the principle for the third year would be = initial deposit + interest for 1st year + interest for the second year
 = 50000 + 3500 + 3745 = $ 57245

Compound interest formula:
The following formula is used to calculate compound interest easily.
CI = A – P,
where
A = P*(1+r)^n,
Where
 P = original principle amount,
 r = rate of interest per conversion period and
 n = number of conversion periods.

Compound interest practice problems:
1. If P = $ 1000, r = 5% p.a. compounded annually, n = 4 years. Find the CI
2. P = $ 16000, r = 10% p.a. compounded half yearly, n = 2 years. Find CI
Answers:
1. $ 215.50 2. $ 3448.10