# Compound Interest and Why It Matters When Investing

Monday, November 5, 2018 | MarketBeat Staff

One of the first lessons we get in compound interest happens around middle school. We are asked the question:  If you could receive one million dollars in one month, or start the month with a penny and double that amount every day, which would you take? The answer shows the power of compounding money.

 Day 1 \$0.01 Day 2 \$0.02 Day 3 \$0.04 Day 4 \$0.08 Day 5 \$0.16 Day 6 \$0.32 Day 7 \$0.64 Day 8 \$1.28 Day 9       ` \$2.56 Day 10 \$5.12 Day 11 \$10.24 Day 12 \$20.48 Day 13 \$40.96 Day 14 \$81.92 Day 15 \$163.84 Day 16 \$327.68 Day 17 \$655.36 Day 18 \$1,310.72 Day 19 \$2,621.44 Day 20 \$5,242.88 Day 21 \$10,485.76 Day 22 \$20,971.52 Day 23 \$41,943.04 Day 24 \$83,886.08 Day 25 \$167,772.16 Day 26 \$335,544.32 Day 27 \$671,088.64 Day 28 \$1,342,177.28 Day 29 \$2,684,354.56 Day 30 \$5,368,709.12

While we all know that compound interest doesn’t work quite this fast, the chart does illustrate the power of compounding interest, and why the time value of money is one of the primary benefits of investing early and consistently. In this article, we’ll take a close look at compound interest, how compound interest is calculated, how frequently interest can be compounded, and why it’s important for investors and borrowers.

What is compound interest?

Compound interest is the interest calculated on an additional principal balance that includes not only the interest on the principal but also the interest on all the interest that has accumulated in the previous period. This is why compound interest is sometimes called "interest on interest". In finance, the alternative to compound interest is simple interest. Simple interest is applied at a specific interest rate at a specific moment in time. A bond that has a 7% yield at maturity would be an example of simple interest. If the par value of the bond was \$10,000, the bondholder would receive \$10,700 at maturity, no matter how long the bond was held for. There would be no compounding done. However, if that same were put into an account where interest was compounded monthly for six months, the growth would look like this:

 End of First Month 10,300 End of Second Month 10,609 End of Third Month 10,927.27 End of Fourth Month 11,255.08 End of Fifth Month 11,592.73 End of Sixth Month 11,940.51

If given the opportunity, everyone would want the option of having the interest on their savings and investments compound. However, one of the things that this example points out is that the frequency of compounding can make a big difference. In fact, more frequent compounding can offset a lower interest rate. For example, what would happen to \$8,000 over one year if the money were placed in a product that compounded at 5% monthly or one that compounded at 10% every six months?

 Product 1 (5% monthly) Product 2  (10% every six months) Month 1 \$8,400 \$8,000 Month 2 \$8,820 \$8,000 Month 3 \$9,261 \$8,000 Month 4 \$9,724.05 \$8,000 Month 5 \$10,210.25 \$8,000 Month 6 \$10,720.76 \$8,800 Month 7 \$11,256.79 \$8,800 Month 8 \$11,819.62 \$8,800 Month 9 \$12,410.60 \$8,800 Month 10 \$13,031.13 \$8,800 Month 11 \$13,682.68 \$8,800 Month 12 \$14,366.81 \$9,680

As you can see, by the fourth month, the account that was compounding monthly was already larger than the account that was compounding every six months would be for the entire year, despite the fact that its interest rate was half of the other.

How to calculate compound interest

To calculate compound interest over a single period, like a month, you simply multiply the principal balance by whatever the interest rate is. Then you take that number and add it back to the principal amount.

As an example, if you were to have \$10,000 in an account that compounded interest at 8% monthly, at the end of the first month the value of your account, assuming nothing was added to the principal would be:

10,000 x .08 = 800 + 10,000 = \$10,800

But you can calculate compound interest over long periods of time. NOTE: you may need a financial calculator to do this. There are also free compound interest calculator tools available online.

However, the formula is:

Compound Interest       = [P (1 + 1n] – P

= P [(1 + i)n-1]

P = Principal; i = nominal annual interest rate as a percent; n = number of periods where compounding interest was calculated

If the \$10,000 account we referenced above was actually a three-year loan with an annual interest rate of 5%. Using the formula, the total interest paid on the loan would be \$1,576.25.

How frequently can interest be compounded?

In theory, interest can be calculated as frequently as someone would want to calculate (daily, weekly, monthly, etc.). In practical terms, there are standard periods for different types of financial products. In general, the interest on a savings account at a bank is typically compound daily, whereas a certificate of deposit (CD) might be daily, monthly or semi-annually. For loans such as mortgages and credit cards, compound interest is normally calculated monthly. This brings to light an important point about compounding. When you are the investor (or the person to whom the interest is owed), more frequent compounding is a benefit. If you are the borrower (or the person who has to pay the interest) you would want less frequent compounding.

Why is compound interest important?

Looking beyond the "what" of compound interest (i.e. more money), it's important to understand why this is important, not only as a consumer but also as an investor. In terms of the potential interest that can be earned, a dollar today is worth more than a dollar earned a month from now. It's why investors should be encouraged to start saving as early as possible. It will simply take less capital on a monthly or yearly basis to accomplish your goals by starting earlier. For example, many financial professionals will illustrate the power of compound interest by using “The Rule of 72: with their clients to show them how soon they can double their money assuming a certain interest rate. The Rule of 72 is a simplified equation whereby the interest rate being received is divided by the number 72 to get the number of years it would take to double an investment.

For example, an \$8,000 investment that has a 5% interest rate would take 14.4 years to double based on The Rule of 72 (72/5 = 14.4). The Rule of 72 assumes that no additional money is being added to the principal balance. Adding money can significantly shorten the time it would take to double the value of an account. This is why many investors can, and should, take advantage of the ability to invest pre-tax dollars into an employer-sponsored account. Not only are you reducing your tax burden, but you are maximizing the advantage of compounding your money.

In reality, most of our investments are not going to pay us compound interest. A bondholder that has a 5% yield on a bond is going to receive 5% above their principal at the maturity date. Likewise, a shareholder who is entitled to receive a quarterly dividend of 4% will receive that dividend based on the market value of his account at that time. The benefits of compounding for investors come primarily through regular and systematic growth in principal. Many long-term investors practice the strategy of dollar cost averaging, which is an ideal way to take advantage of the time value of money. By continuing to buy shares on a regular basis, regardless of price, investors can take advantage of price swings and can see their account grow over time. Because stocks and other equities tend to have a higher rate of growth than bonds or cash, the effect on a portfolio is similar to that of compound interest. In both cases, you are allowing the time value of money to work for you.

How to track the compound growth of your portfolio?

One of the tools that fund managers may use to track the performance of a mutual fund's growth over time is the Compound Annual Growth Rate (CAGR) formula. This will be listed as a percentage in most fund prospectuses so we won't go into the entire formula here, but it's useful for investors to understand whether or not the fund they are in is beating the market, even with the market, or falling behind the market. If a market index has consistently delivered an 8% return over five years and your fund is only returning 5%, then the fund is underperforming. If the numbers are reversed, then your fund is outperforming the market. In both cases, it's helpful to understand why that is the case.

For example, a fund may be outperforming the market because it is shifting its asset allocation into riskier components. Investors with a lower risk tolerance may find this to be a risk they don't want to take and will look to shift their money into something more conservative. Likewise, a fund that appears to be underperforming may, in fact, have shifted some assets in anticipation of a market correction. In this case, your funds may be better served staying where they are and rely on dollar cost averaging to boost the value of your portfolio over time.

Whether you are an aggressive or conservative investor always remember that when it comes to compounding your money, time is your biggest ally.

Compounding interest as a borrower

When you take out a loan, compounding interest can be your enemy or your friend. Certainly, if you can afford to pay back the loan immediately, or if you are planning on paying significantly more than the required minimum every month, then you will be greatly reducing your interest payments if they are calculated using a compound interest schedule as opposed to a simple interest. For example, if you have a \$5,000 with 5% annual percentage rate (5%), you would be charged five percent of the principal balance for every month you have the loan. So, the first month your interest payment would be approximately \$21. As you pay down the principal, the interest would be less because the principal would be lower. For a simple interest loan, the interest payment will remain the same, no matter what the principal balance is.

One thing that borrowers should be mindful of is if the loan has a variable rate. This allows the creditor to adjust the interest rate higher if interest rates move higher. Of course, this can be to your benefit if interest rates fall, but in general, this is something to be wary of, particularly if you know you will have to be paying the loan off over time.

The bottom line on compound interest

Albert Einstein referred to compound interest as the eighth wonder of the world and it's easy to see why. Compound interest is more reliable than finding the next Amazon or Google. It just relies on having to be a consistent investor and allowing the time value of money to work for you.

Compound interest is more about frequency than it is about a particular interest rate. For example, in some cases, you can achieve a greater benefit from an account where interest compounds monthly at a lower interest rate than one that compounds semi-annually with a higher interest rate. As important as the financial benefit (the “what”) that comes from compound interest, it’s important to understand that time truly is your biggest ally. A dollar that you put in today will be worth significantly more than a dollar invested a month or a year from now. Compounding is also something that can be measured when you are looking at the performance of a mutual fund. By calculating the funds Compound Average Growth Rate (CAGR), you can see if your fund is outperforming or underperforming, which can help you make an informed investment decision.

Compound interest is something that can work to your benefit or to your detriment when you are the borrower. If you are going to pay the loan off quickly, or are sure you can always pay more than the minimum owed, compounding interest can help ensure you are paying less over the life of the loan. However, because of compounding, variable interest rates on loans or credit cards can significantly impact your borrowing costs.

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