# How to Calculate Compound Interest

Compound interest is the process of adding interest to the initial amount of an investment, and from then on earning further interest on this new amount. This is distinct from simple interest, in which the rate is applied once to the initial amount and then multiplied by the term of the investment.

The vast majority of investment vehicles offer compound interest.

Calculating compound interest is not as straight forward as simple interest, although it is not particularly difficult once the underlying formula is known. The remainder of this article outlines the method to use.

In order to make the calculation it is necessary to know both the periodic rate of interest and the compounding period. Given these two facts it is possible to determine the return on investment over a given period, as well as a nominal annual rate and annual percentage rate (APR), two means of comparing investments offering different compounding periods.

Compounding periods will generally be one of daily, monthly, quarterly or yearly, although technically any fixed period is possible.

For instance a compounding period of monthly and periodic rate of 1% means every month interest is calculated at 1% and added to the principal (initial amount). This is the same as an account that has a monthly compounding period with a 12% nominal annual interest rate (12% / 12 months = 1%).

Definition of terms:

PV = present value of a sum (initial investment, or principal)
FV = future value of a sum (the total balance at the end of a given period)
i = the periodic rate of interest
n = the number of compounding periods in a sum

The formula to calculate the future value of an initial investment is then:

FV = PV(1 + i)^n

In the formula ^ means to the power of. For instance 2^3 is 2 to the power of 3, which is 8.

For example what is the future value of investing \$1,000 for 10 years at a nominal annual rate of 12% given a compounding period of monthly?

PV, the present value is \$1,000
i, the periodic interest rate is 12% / 12 months = 0.12 / 12 = 0.01
n, the number of compounding periods, is 10 years 12 months = 120 months

So plugging in the numbers:

FV = 1000 (1 + 0.01)^120 = \$3,300.39

In other words, the investment returns \$2,300.39 in interest over the ten years.

Although it is straight forward to calculate compound interest this way it is also possible to use an online calculator.

Alan Cameron lives in Adelaide, South Australia. He is a full-time mathematician and part-time investor.

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# Understanding Compound Interest

With all of the financial terms in the world, it seems that few are more confusing than compound interest. Perhaps it is the name that leads people to misunderstand exactly how it is that compound interest works, or maybe it’s the formula that is used to compute it. Compound interest doesn’t have to be confusing, however; the information below should answer most if not all of your questions concerning compound interest and how it can affect you.

What Is It?

Compound interest is simply interest that is collected both on the principal (the original amount) and the interest that has already been applied to the principal. This means that each time interest is applied to the amount (also known as being compounded), the amount of interest compounded will be added to the principal for the next time that the interest is compounded. To put it more simply, compound interest means that every time interest is applied, it is applied based upon the entire amount instead of just the principal.

What Does It Do?

Since compound interest is applied to all of the money held within the account being compounded, this means that as time goes by more money will accumulate within the account because each increase will subsequently increase the amount being paid. This is most often the case in savings accounts and interest-bearing chequeing accounts, as well as with the interest due on many loans.

How Is It Calculated?

The formula for calculating compound interest is written as A = P(1 + r) n, with A being the amount of money accumulated after the interest is compounded, P being the principal amount of deposit, r being the annual rate of interest, and n being the number of years over which interest is collected. If the interest is being compounded more regularly than once per year, the r is divided by the number of times that the interest is being compounded (for monthly interest, this would be 12 times, and for daily interest it would be 365 times.) As an example, imagine P being 100, on 5 percent interest (compounded monthly), over a period of 5 years. This would look like A = 100(1 + 5/12) 5, or 100 x (1 + 5/12), with the portion in brackets multiplied by itself 5 times.

How Does It Work For You?

Since compound interest pays additional interest money based upon the interest that has already been paid, this means that as time goes by you will be making a significant amount of money simply from having your principal deposit in your savings or other bank account. You should be sure to keep in mind that many banks and other lenders use compound interest on their loans as well, so that the longer that you take to repay the loan then the more you will have to repay. This can be an incentive to repay debts during a grace period, or at least to do your best to pay off the debt as early as possible so that you can save as much money as you can.

Finding the Best Rates

In order to find the best loan rates, it’s important to take the time to shop around and explore your various options concerning the type of account or loan you’re looking for. Request rate quotes and compare them to each other to ensure that you get not only a rate that you’re satisfied with but also the best rate that you can get.

# How Compounding Interest Works

Compounding money or compound interest is the fastest and easiest way to make money. There are two ways to compound money and they are through investing and building a business. In your checking or savings account, you may notice that you make interest on your money. This money gets compounded, meaning that you earn interest on top of interest you have already earned. This is called compound interest and is the fastest and easiest way to make money. You can literally make money by doing nothing. These interest rates are very small, but they add up over time.

Say you have \$1,000 and your bank interest rate is 1%. At the end of the year, you will have an extra \$10 in our account from interest. After 10 years, you will have an extra \$100 in your account from simple interest. That, however, is simple interest. Compound interest earns interest on top of the interest you have already owned. So instead of having \$1,100 after 10 years, you will have \$1,104.62. To see this, take \$1,000 x1.01 and multiply whatever answer you get by 1.01 and do that ten times. This concept carries over to the stock market and mutual funds. Since the stock market and mutual funds generate returns far greater than 1%, compound interest can make you a lot more money.

Now first off, don’t be afraid of the stock market. When people hear of the stock market the first thing they think of is that they are going to lose all their money, but that isn’t true. The stock market has averaged about a 10% annual return every year since it has existed. It will have its ups and downs so pick a good safe mutual fund so that you are well diversified and don’t have to do your own trading. Say you invest \$10,000 over a couple of years and get the average 10% return. After 10 years, with simple interest, you will have \$20,000, because you will have gained an extra \$1,000 every year.

With compound interest, however, you gain much more. In fact, you will have \$25,937, which is an increase of \$6,000 dollars from simple interest. In fact, in 10 years, you will have gained \$16,000 by doing nothing. Keep dumping money in and holding the money for longer periods of time, and you will have an astronomical amount of money. This is the magic of compound interest. Building a business is another way to compound money. Did you know that if you had \$100 and gained a 20% profit every week; that you will have over \$1 million by the end of the year? If you don’t believe me, do the math. Take \$100 x1.2 and multiply whatever answer you get 51 times. It is astonishing.

What you do is start out small and then keep reinvesting that money back into your business. Say you bought a broken bike for \$100. You fixed it up and now sell it for \$120. That is your 20% profit right there. Now, you take that \$120 and buy another bike and fix that one up too. You sell that one for \$144 and again you have a 20% profit. You keep repeating this over and over. Eventually you will have to move up into more expensive categories. Say you bought a car for \$10,000 and fixed it up. Now you can sell it for \$12,000 and that is your 20% profit. Re-invest that in your business and keep compounding money until you are financially secure. Compounding money is the fastest and easiest way to become financially secure. Anyone can do it through smart investing or through building a business. Do both of these at once, and you can live the life you’ve always wanted to in no time.