Compound interest affects far more than just the interest you earn on a bank account. To create wealth over the long term it is crucial to understand how compounding affects all your investments as well as any debt you might have.

- What is compound interest?
- What does compound interest affect?
- Why is compound interest so powerful?
- Compounding frequency
- Calculating compound interest
- How compound interest applies to stock market investing
- Pros and cons of compounding

### What is compound interest?

Compound interest is simply the interest you earn on interest you have already earned. Compounding is the cumulative effect of earning interest on previously earned interest. As an example, imagine you put $100 in a savings account earning an annual interest rate of 5% for 10 years:

If the interest was calculated at the end of those 10 years, it would simply be $100 x 5% x 10 years which is $50. You would then have $150 in your account. If it was calculated at the end of each year, and the interest earned for the year was added to the original $100, the interest amount would increase each year, as follows:

Year 1: $100 x 5% = $5

Year 2: $105 x 5% = $5.25

Year 3: $110.25 x 5% = $5.51

Etc…

The interest paid after the 10^{th} year would be $7.75, and in total you would have $162.89 in your account. Using the first method would result in a return of 50%, or 5% a year. The second method would give you an overall return of 62.89%, or 6.3% a year, even though you were still earning 5% on the capital in your account each year. The compounding effect would increase even more if interest was compounded monthly, weekly or daily. The more frequently interest is compounded, the higher the effective interest rate.

The effective interest rate is the amount you end up earning from an investment due to the compounding effect. It depends on the frequency, interest rate and the term of the investment. Compounding is not just applicable to interest, but to growth and returns too.

### What does compound interest affect?

Compound interest is the basis for the most fundamental principal in finance, *‘time value of money.’ *The compound interest formula is used to calculate the difference between the future value (FV) and the present value (PV) of an asset. This principle underpins nearly every calculation used in finance and investing.

As well as the interest earned in a bank account, the principal of compounding affects the interest on loans, inflation and the returns on any type of investment. Inflation also compounds over time. That means the buying power of money decreases exponentially. This is why investing and earning returns that are higher than inflation is necessary to preserve spending power. When it comes to stock investing, the compounding effect is used to value companies, asses the way they use retained earnings and debt, and to calculate portfolio returns.

Bond investing is based on the same concepts. When it comes to investing for retirement, the same inputs that are used to calculate compound interest, are the ones that will determine the size of retirement account. Financial planners use asset allocation to construct portfolios that will outperform inflation. Compounding is also used to calculate mortgage payments and has implications for tax planning.

### What makes compound interest so powerful?

Albert Einstein famously said that the principle of compounding was the most powerful force in the world. He may well have been right. Compounding leads to exponential growth. In other words, any amount subject to compounding interest or growth will grow at an accelerating rate. The chart below shows how $100 will grow over 20 years, with daily compounding and an annual growth rate of 10% or 20%.

The higher the rate of growth, the faster the growth will accelerate. In this example, with a growth rate of 10%, the growth in year 20 is equal to 70% of the original amount. However, with a 20% growth rate, the growth rate in year 20 is equal to 988% of the initial $100!

The fact that compound interest is so powerful, is one of the reasons it’s difficult to create wealth solely by earning a salary. A salary, especially one that only grows at the rate of inflation, doesn’t give one leverage. By contrast, saving and investing allows capital to multiply. Twenty to thirty years compound returns can turn a modest amount invested in a diversified portfolio into a sizable nest egg.

### Compounding frequency

A savings account earning the same interest rate will grow faster as the compound frequency increases. The following table illustrates the effect of simple interest vs. compound interest with different compounding periods. The original example of $100 earning 5% a year for 10 years is used.

In the case of most banks and financial institutions, interest is calculated daily, but only credited to the account at the end of the month. The same applies to the interest payments paid on credit card debt.

### Calculating compound interest

The following compound interest formula is used to calculate the accrued interest and principal:

A = P x (1 + r/n)^{nt}

Where,

A = Total amount (principal and interest)

P = Principal (starting amount)

r = Annual interest rate as a decimal

n = Number of compounding periods per year

t = Number of years

Using the example, we started with, the formula looks like this because we compounded annually:

A =100 x (1 +
0.05/1)^{10 }= 162.89

If we compounded monthly, it would look like this:

A =100 x (1 +
0.05/12)^{12*10} = 100 x (1 + 0.0042)^{120 }= 164.70

To calculate the accumulated interest, you must subtract the original principal from the total amount. You can also calculate the effective interest rate by dividing the accumulated interest by the number of years, and then dividing the result by the original principal. If you want to create a compound interest calculator in Excel, you can use the following formulas:

Total amount=P*(1+i)^n)

Interest amount = ((P*(1+i)^n) – P)

The *rule of 72* is a quick and easy way to calculate roughly how long it will take for a given amount of capital to double for any given annual interest rate. For example, if the interest rate is 10%, it will take 72/10, or 7.2 years to double your money. If you earn 3%, it will take 72/3, or 24 years to double your money.

### How compound interest applies to stock market investing

The principle of compounding applies to the stock market too. If a company can earn 20% on any capital it uses, then retained earnings can be compounded very quickly. This is how companies that grow rapidly can get so big so quickly. Companies like Facebook and Google became some of the biggest companies in the world in a short period for two reasons. Firstly, they have high margins and make big profits. And secondly, they are able to quickly deploy retained earnings to earn the same high margins.

Most investors like to receive dividends. However, if a company is able to earn high rates of return, it’s actually better for them to reinvest the profits rather than paying them out. For investors to enjoy the full benefits of compounding, they should reinvest dividends from the most profitable companies in their portfolios.

Higher returns come with higher risks. However, compounding can allow a high-risk investment to produce exceptional returns over the long term. Within a diversified portfolio, a small amount invested in riskier assets can create exceptional returns over time.

When looking at portfolio returns over periods of more than one year, investors use the CAGR, or compound annual growth rate. If a portfolio grows from $100,000 to $200,000 in 5 years, it has effectively grown each year by 20% of the original value. However, this doesn’t account for the fact that returns have compounded. The CAGR removes the compounding effect to calculate the average return without compounding. It can be calculated as follows:

CAGR = (Ending
value/Beginning value)^{ (1/years) }-1

So, for the above example, we have:

CAGR =
(200,000/100,000)^{0.2} -1, or 14.86%.

A $100,000 portfolio growing on average at 14.86% for 5 years will be worth $200,000. This calculation is used extensively by financial planners when calculating required growth rates.

### Pros and cons of compounding

The continuous compounding of returns is the reason that, given long enough, a retirement account with fairly modest contributions and annual returns can grow into a sizable nest egg. Research has shown that stock market total returns (price and dividends) vastly outperform price returns. However, this is only true if dividends are reinvested. This shows how important compounding is to stock market returns.

The disadvantages of compounding relate mostly to debt. Borrowing money at a high interest rate, or missing payments can very quickly lead to the amount owed snowballing. A manageable loan can quickly become impossible to service. This often leads to the downfall of companies, and even countries.

Stock market volatility means that a portfolio that has grown over decades can be reduced by 30% or more in a matter of months. The capital that is lost may have taken decades to reach the levels it did – and may take as long to rebuild. This is why investors need to manage risk carefully as they approach retirement age.

### Conclusion: Invest and take advantage of compounding

Compounding is indeed a powerful force, and one that any investor needs to use to their advantage. As illustrated, eventual returns depend not just on the rate of return, but the time period and the frequency at which returns are compounded. That means that the earlier an investor begins saving, the faster their portfolio can eventually grow.

It also means that companies that can redeploy profits quickly, can compound earnings very quickly. The principle of compounding also shows why debt needs to be carefully managed, the importance of managing portfolio volatility through asset allocation and diversification.

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