Compound Interest Formula

Tutorial and Worksheet for Teaching Yourself

The Power of Compound Interest
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There are two types of interest, simple and compound. Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Learn more about compound interest, the math formula for calculating it on your own, and how a worksheet can help you practice the concept.

More About What Compound Interest Is

Compound interest is the interest you earn each year that is added to your principal, so that the balance doesn't merely grow, it grows at an increasing rate.

It is one of the most useful concepts in finance. It is the basis of everything from developing a personal savings plan to banking on the long-term growth of the stock market. Compound interest accounts for the effects of inflation, and the importance of paying down your debt.

Compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount.

For example, if you got 15 percent interest on your $1000 investment the first year and you reinvested the money back into the original investment, then in the second year, you would get 15 percent interest on $1000 and the $150 I reinvested. Over time, compound interest will make much more money than simple interest. Or, it will cost you much more on a loan. 

Computing Compound Interest

Today, online calculators can do the computational work for you.

But, if you do not have access to a computer, the formula is pretty straightforward.

Use the following formula used to calculate compound interest:

Formula

M = P( 1 + i )n

MFinal amount including the principal
PThe principal amount
iThe rate of interest per year
nThe number of years invested

Applying the Formula

For example, let's say that you have $1000 to invest for three years at a 5 percent compound interest rate.

 Your $1000 would grow to be $1157.62 after three years.

Here's how you would get that answer using the formula and applying it to the known variables:

  • M = 1000 (1 + 0.05)3 = $1157.62

Compound Interest Worksheet

Are you ready to try a few on your own? The following worksheet contains 10 questions on compound interest with solutions. Once you have a clear understanding of compound interest, go ahead and let the calculator do the work for you.

History

Compound interest was once regarded as excessive and immoral when applied to monetary loans. It was severely condemned by  Roman law and the common laws of many other countries.

The earliest example of a compound interest table dates back to a merchant in Florence, Italy, Francesco Balducci Pegolotti, who had a table in his book "Practica della Mercatura" in 1340. The table gives the interest on 100 lire, for rates from 1 to 8 percent for up to 20 years.

Luca Pacioli, also known as the "Father of Accounting and Bookkeeping," was a Franciscan friar and collaborator with Leonardo DaVinci. His book "Summa de Arithmetica" in 1494 featured the rule for doubling an investment over time with compound interest.