Define compound interest:
You already know how to calculate simple interest, but in normal business circles simple interest is very rarely used. For example, if a man deposits $ 1000 in a bank that earns him an interest of 5% per year. At the end of one year, the money earned by him would be $ 50.
However, unless he takes out his $ 50 in cash, it will be added to his original $ 1000. Thus, if he leaves his money in his account, in the next year the bank will be paying him interest on his original $ 1000 plus the $ 50 interest, i.e. $ 1050.
In the third year the interest will once again be added to the new principal of $ 1050, and so on for as long as the money is left in the account.
This kind of interest is known as compound interest. Some banks and other institutions pay interest yearly, others every six or even after every three months.
Thus we can define the compound interest as the interest that accrues when earnings of each specified period of time is added to the principal thus increasing the principal base on which the subsequent interest is computed.
Compound interest calculation:
Compound interest problems can be solved using two methods.
(a) Using the simple interest formula.
Example: Principal amount = P = $ 5000, time period = n = 2 years and rate of interest = r = 10% compounded annually.
Solution: Interest for the first year = Prn = 5000 * 10/100 * 1 = $ 500
Principal at the end of the first year = 5000 + 500 = $ 5500
Interest for the second year = Prn = 5500 * 10/100 * 1 = $ 550
Therefore total interest earned in two years = 500 + 550 = $ 1050
This method however is very cumbersome for longer periods of time. Therefore we use the next method.
(b) Using the compound interest formula.
This formula can be used for any number of conversion periods per year and for any number of years. The formula is as follows:
CI = A – P,
Where A = P * (1+r/n)^nt
Here, A = amount at the end of t years
P = original principal amount
r = nominal rate of interest
n = number of conversion periods per year.
[Note that n = 1 for interest compounding annually, n = 2 for interest compounding semi annually, n = 4 for interest compounding quarterly and so on]
(c) Continuous compound interest formula:
CI = A – P
A = Pe^rt