Compound interest is the interest that accumulates on the principal amount of money plus any interest that has been earned during the course of a loan, deposit or debt. Unlike simple interest, which only accrues on the principal, compound interest accrues on both the principal and interest combined. When interest is compounded, the principal amount grows faster than it would under simple interest. In most cases, interest is calculated on a yearly basis, but the terms may vary among financial institutions. The compounded interest grows higher when interest is added to the principal on a frequent basis. Compound interest is beneficial because it allows for a higher return on the initial monetary investment.
Compound interest is calculated by figuring out the amount of interest for the present value of the investment and then adding that amount to the principal. The new dollar amount can be multiplied against the projected number of years of the investment. This figure will be the total amount earned after the time period is up.
The base formula for calculating interest for one year is:
A = P(1+r)
A is the future value, P is the starting principal and r is the interest rate as a decimal.
The formula for calculating annually compounded interest for multiple years is:
A = P(1+r)Y
Where Y is the number of years to compound over.
If we put $1000 in a term deposit for 5 years at 5.5% we get the equasion:
A = 1000(1+0.055)5
At the end of 5 years we would have $1,306.96.
If you would like to compound more often than annually, you need to modify the equation like so:
A = P(1+r/n)Yn
Where n is the number of times you want to compound each year.
If our $1000 deposit above was compounded monthly instead of annually, we would have:
A = 1000(1+0.055/12)60
At the end of 5 years we would now have $1,315.70.
See also our compound interest calculator.
Simple interest is the interest that is earned on the principal amount of money over a certain amount of time. In this case, interest only accrues on the original amount of money that is loaned, borrowed or deposited. The simple interest on a loan is calculated by multiplying the principal amount by the rate of interest and the amount of time on the loan.
The formula for calculating simple interest is:
I = Prn
I is the interest earned, P is the principal amount, r is the interest rate as a decimal, and n is the number of years remaining on the loan.
For example, if a person lends $10,000 for five years at the rate of 5 percent, we get:
I = 10000 X 0.05 X 5
In other words, this person will earn $2,500 in interest during the course of the loan.
See also our simple interest calculator.