Simple interest is paid on only the principle of the investment or loan (the money originally invested or borrowed). If a person invests $1000, for instance, at an interest rate of 2.5 percent (simple interest) for two years, we can easily find the amount of interest paid by using the following formula:
The “I” stands for simple interest, the “P” for the principle amount invested or loaned, the “r” for the interest rate (expressed as a decimal), and the “n” for the length of the investment or loan.
If we plug in the numbers from our example, then, we have
Performing the calculations, we discover that the investment earns $50 in simple interest over two years.
Compound interest, on the other hand, is paid on both the principle and the already accrued interest of an investment. In other words, if the same person invests $1000 at an interest rate of 2.5 percent (compound interest) for two years, the investment will earn interest in the first year, and that interest will be counted toward the interest calculation in the second year of the investment. The investment is essentially paying interest on the interest already earned.
The formula for calculating compound interest looks like this:
`I=P xx (1 + r)^t - P`
“I” again stands for interest, only this time we are calculating compound interest. “P” is principle; “r” is the interest rate (again expressed as a decimal); and “t” is the time of the investment.
If we plug in the numbers, we have
When we perform the calculations (following the necessary order of operations), we find that the compound interest earned on the investment over two years is $50.63.