“The Magic of Compounding” is a term that has become popular in investing circles, but what exactly is it and how can it help you? This post will explore compound interest and its implications for both investors and borrowers.

## What is Compound Interest?

Investopedia defines compound interest as *“interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan”. *The key part of the definition is *“the accumulated interest from previous periods”*. In layman’s terms, this essentially means the interest is earning interest.

Compound interest can work for and against you. Naturally, you want your investments and deposits to be accruing compound interest while you don’t want compound interest on your loans.

## Compound Interest Vs. Simple Interest

When dealing with investments and loans there are two main interest types. Simple interest and compound interest. We have defined compound interest above. Simple interest is essentially the same but the principal used to calculate the interest does not take into account any interest from the previous periods.

As a general rule, for investments, we want to take advantage of compound interest, and for loans, we want to pay simple interest. The examples below should highlight this point. We will keep this basic and assume the interest is compounded once a year. I’m not going to go into detail with formulas for calculating compound interest, a google search will provide you with plenty of calculators.

Compound Interest Investment

Principal = €1,000

Interest Rate = 10%

Term = 3 Years.

Return / Total after year 1 = €100 / €1,100

Return / Total after year 2 = €110 / €1,210

Return / Total after year 3 = €121 / €1,331

Simple Interest Investment

Principal = €1,000

Interest Rate = 10%

Term = 3 Years

Return / Total after year 1 = €100 / €1,100

Return / Total after year 2 = €100 / €1,200

Return / Total after year 3 = €100 / €1,300

Although there is only €31 in the difference, it is a relatively small principal amount and a short period of time. Granted the interest rate is probably higher than you could attain in today’s market, but it is only used for ease of calculations. If this was your retirement portfolio, the €31 would be a lot bigger. It is essentially free money. Using the same numbers as above but over 25 years, the difference between the simple and compound interest earned would be €7,334.71!

The above numbers can be flipped for a loan. If you were taking out identical loans using the principal and terms above, the compound interest loan would cost you an additional €31 over the life of the loan. Again it is not a substantial amount but is a relatively low principal amount.

## Compounding Frequency

In the above example, we assumed that the loan or investment compounds once a year. The more often it compounds, the greater the amount of interest payable. This is due to the fact that each compounding period will take the interest of the previous periods into account. Let’s use the above example but instead of compounding once a year, we will assume the interest is compounded semi-annually or twice a year. The easiest way to think of this is that instead of earning 10% once a year, you earn 5% twice a year with the second 5% taking into account the interest of the initial 5%.

Compound Interest Investment (Semi-annual compounding)

Principal = €1,000

Interest Rate = 10%

Term = 3 Years.

Return / Total after year 1 = €102.50/ €1,102.50

Return / Total after year 2 = €113.01 / €1,215.51

Return / Total after year 3 = €124.59 / €1,340.10

Again, not a huge difference but one worth keeping in consideration (particularly when dealing with loans).

## Useful Formulas

There are some useful compounding formulas you can use when planning for your future.

Rule of 72

The *Rule of 72* is a rough estimate that calculates how long it will take an investment to double in value at a given rate of interest. It is as simple as dividing 72 by the annual rate of return. For example, an investment growing at 8% per year will take 9 years to double. This formula can only be used for annual compounding.

Compound Annual Growth Rate (CAGR)

The CAGR is useful when you are trying to determine the rate of return you have gotten over a specified period of time. As you can tell from the acronym, it provides you with an annual return rate. It is useful when trying to benchmark your returns against the market or specific funds. If you believe you can beat the market over a specific period of time, CAGR will be able to prove or disprove it. Again, I won’t give the formula here as there are a plethora of them available on the internet, but I will give an example.

Principal = €1,000

Term = 3 Years

Final Value = €1,400

CAGR = 11.87%

## Compounding Investments

Compounding interest is a great tool if you can use it, however, most interest-paying investments work on a simple interest formula. Zero-Coupon Bonds are the most widely accessible interest-paying investment that works on a compounding basis (via a discount to the bond price at the outset). The easiest way for the average investor to take advantage of compounding is through a mutual fund or a brokerage plan that reinvests interest/dividends.

When dividends are paid they are automatically used to purchase more shares in the fund. These additional shares will provide extra dividend income which is, in turn, reinvested, compounding over time. A key point to be aware of is that dividend payments are usually taxable unless you are using a pension account or tax-sheltered account. Make sure you are being fully tax compliant when reinvesting dividends, it may lower your return but it also lowers the risk of penalties.

## The Power of Compounding

As we have seen, compounding interest and investments can be a powerful way to increase your rate of return. The best time to begin compounding is now and we can highlight this with a simple example. A common misconception held by amateur investors is that if they invest in a year rather than now, they will only miss out on the returns for the first year. This isn’t true.

Let’s take two investors, Investor A and B. Both will invest in identical compounding portfolios with identical rates of return, but Investor A decides to invest now rather than next year. Let’s also assume they share a retirement date and will sell their portfolios on this date. (I’ll keep the investment horizon short for simplicity).

Starting Principal = €100,000

Rate of Return = 5%

Retirement Date = 01/01/2025 (5 years for Investor A, 4 years for Investor B when he invests in 2021).

Investor A Yearly Totals

Year 1 Return / Total (2020) = €5,000 / €105,000

Year 2 Return / Total (2021) = €5,250 / €110,250

Year 3 Return / Total (2022) = €5,512.50 / €115,762.50

Year 4 Return / Total (2023) = €5,788.13 / €121,550.63

Year 5 Return / Total (2024) = €6,077.53 / €127,628.16

Investor B Yearly Totals

Year 1 Return / Total (2021) = €5,000 / €105,000

Year 2 Return / Total (2022) = €5,250 / €110,250

Year 3 Return / Total (2023) = €5,512.50 / €115,762.50

Year 4 Return / Total (2024) = €5,788.13 / €121,550.63

As you can see, the year missed by Investor B has cost him €6,077.53, not €5,000. He is missing out on the final years’ return, not the initial year. This is an important point to take away, by delaying your investment by a year you miss out on the final years’ return, not the initial year. It is important to invest as soon as possible. The example above is based on a short time frame, with the power of compounding the difference a year makes will be magnified the longer the investment horizon.

If we use the same example but over 25 years, Investor A’s portfolio would be worth €338,635.49 while Investor B’s portfolio would be worth €322,509.99, a difference of €16,125.50!

Compounding is a powerful tool but unless you invest wisely you won’t reap the full benefits it has to offer. As always, before investing in anything do your research.

*The Stoic Trader. *

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