Hi, I'm Jen D'Amore for About.com, and this video is all about how to calculate compound interest.

Definition of Compound Interest

What is compound interest? It's interest paid on both the principal amount and on any interest earned. So the amount of interest earned increases over time, because it's being calculated from a larger principle amount.

Compounding yields a greater return than simple interest, and being able to calculate it can really help make decisions about an investment.

Example of Simple Interest Versus Compound Interest

Here's an example of the same amount calculated with simple interest, and with compounded interest. $1000 invested at a flat rate of 5% yields $1050, since 50 is 5% of 1000. But that same $1000 invested for 3 years at a rate of 5% compounded interest yields $1157.62, a difference of $107.62.

The larger the principle and the longer the investment, the greater the interest earned. Not only are you earning interest on the original, or principle amount, but you're earning on the interest that's been added to your principle amount.

Basic Formula to Calculate Compound Interest

Here's the basic formula to calculate compound interest: P(1 + i)^n = M. P is the principal amount - the amount you originally invest, iis the rate of interest per year (expressed as a decimal), n is the number of increments of time (in this case, years) invested, and M is the final amount, including the principal.

Using the $1000 from before, the equation would look like this: 1000 (1+0.05)^3 = 1157.62.

Additional Example of Calculating Interest Compounded Annually

Here's another example. $10,000 invested for 50 years earning 4% compounded annually: 10,000 (1+0.04)^50 = $71,067. $10,000 invested for the same 50 years earning 12% interest compounded annually is: 10,000 (1 + 0.12)^50 = $2,890,022.

Formula to Calculate Interest Compounded More Frequently

It's also possible to have the interested compounded more frequently than annually. Compounding quarterly compounds the interest earned every 3 months, every quarter of a year. To calculate that, use a slightly different formula: P (1 + r/n)^nt = M.

Just as in the basic compounding formula, P is the principal amount or your initial investment, r is the annual interest rate converted to a decimal, n is going to be the number of times the interest is compounded per year, in this case 4, and t is the number of years.

Examples of Calculating Interest Compounded Quarterly

So, to figure out what a $10,000 investment earning an annual 4% interest compounded quarterly would be after 50 years, plug everything into the equation: 10,000 (1 + 0.04/4)^(4x50) = 73,160.

It would total over $73,000 when compounded quarterly compared to just over $71,000 when compounded annually. That certainly demonstrates the power of compounding interest.

Thanks for watching. To learn more, visit us on the web at About.com.

Definition of Compound Interest

What is compound interest? It's interest paid on both the principal amount and on any interest earned. So the amount of interest earned increases over time, because it's being calculated from a larger principle amount.

Compounding yields a greater return than simple interest, and being able to calculate it can really help make decisions about an investment.

Example of Simple Interest Versus Compound Interest

Here's an example of the same amount calculated with simple interest, and with compounded interest. $1000 invested at a flat rate of 5% yields $1050, since 50 is 5% of 1000. But that same $1000 invested for 3 years at a rate of 5% compounded interest yields $1157.62, a difference of $107.62.

The larger the principle and the longer the investment, the greater the interest earned. Not only are you earning interest on the original, or principle amount, but you're earning on the interest that's been added to your principle amount.

Basic Formula to Calculate Compound Interest

Here's the basic formula to calculate compound interest: P(1 + i)^n = M. P is the principal amount - the amount you originally invest, iis the rate of interest per year (expressed as a decimal), n is the number of increments of time (in this case, years) invested, and M is the final amount, including the principal.

Using the $1000 from before, the equation would look like this: 1000 (1+0.05)^3 = 1157.62.

Additional Example of Calculating Interest Compounded Annually

Here's another example. $10,000 invested for 50 years earning 4% compounded annually: 10,000 (1+0.04)^50 = $71,067. $10,000 invested for the same 50 years earning 12% interest compounded annually is: 10,000 (1 + 0.12)^50 = $2,890,022.

Formula to Calculate Interest Compounded More Frequently

It's also possible to have the interested compounded more frequently than annually. Compounding quarterly compounds the interest earned every 3 months, every quarter of a year. To calculate that, use a slightly different formula: P (1 + r/n)^nt = M.

Just as in the basic compounding formula, P is the principal amount or your initial investment, r is the annual interest rate converted to a decimal, n is going to be the number of times the interest is compounded per year, in this case 4, and t is the number of years.

Examples of Calculating Interest Compounded Quarterly

So, to figure out what a $10,000 investment earning an annual 4% interest compounded quarterly would be after 50 years, plug everything into the equation: 10,000 (1 + 0.04/4)^(4x50) = 73,160.

It would total over $73,000 when compounded quarterly compared to just over $71,000 when compounded annually. That certainly demonstrates the power of compounding interest.

Thanks for watching. To learn more, visit us on the web at About.com.

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