What Is Compound Interest?
Question
Which is the correct formula for calculating compound interest?
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Hi, my name is Bassem Saad, and I'm an associate math instructor and Ph.D. candidate, and I'm here today for about.com to answer the question "What is compound interest?"
Definition of Compound Interest

Compound interest is the money earned from an investment or a fee charged for money borrowed. At each time interval, a percentage of the outstanding balance is added. If no money is taken away, the balance will grow unchecked.
Examples of Compound Interest

So our first example will be compounded annually, where investment (P) is compounded annually, at a rate (r) for (t) years. From this, we get this formula: A = P (1+r)^t, where P is the principle or initial investment, or initial money borrowed; r is the interest rate; t is the number of years; and A is the balance after t years. If we invest \$3,000 at a rate of five percent, compounded annually for 20 years - \$3,000, at a rate of five percent, for 20 years, we'll have \$7,960.

So if the interest rate is paid more frequently than annually, then we would need to use different formulas. If the interest rate was paid quarterly, that's four times a year, then you would take the same formula but divide the rate by four and multiply the time by four. If it was monthly, you would take again the same formula, but divide the rate by 12, multiply the time by 12. And if there were n periods, you'd want to divide the rate by n and multiply the year by n.

So if we want to invest \$3,000 compounded monthly at an interest rate of five percent for 20 years. We have the principal at \$3,000, we have r equals .05, we have the t equals 20, and we plug it into the monthly equation up here to get a grand total of \$8,138. So now we know what compound interest is.