Why compound interest

To calculate compound interest over a certain period of time, here is a mathematical formula you can use:. Where "A" is the final amount, "P" is the principal, "r" is the interest rate expressed as a decimal, "n" is the compounding frequency, and "t" is the time period in years. Here's what all of these variables mean:. In the previous example, we used annual compounding -- meaning that interest is calculated once per year.

In practice, compound interest is often calculated more frequently. Common compounding intervals are quarterly, monthly, and daily, but there are many other possible intervals that can be used. The compounding frequency makes a difference -- specifically, more frequent compounding leads to faster growth. In this case, "n" would be four since quarterly compounding occurs four times per year.

From this information, we can calculate the investment's final value after 20 years like this:. The difference between compound interest and compound earnings is that compound earnings refers to the compounding effects of both interest payments and dividends, as well as appreciation in the value of the investment itself.

When these dividends and price gains compound over time, it is a form of compound earnings and not interest since not all of the gains came from payments to you. In a nutshell, when you're talking about long-term returns from stocks , ETFs , or mutual funds , it's technically called compound earnings, although it can still be calculated in the same manner if you know your expected rate of return.

Compound interest is the phenomenon that allows seemingly small amounts of money to grow into large amounts over time. In order to take full advantage of the power of compound interest, investments must be allowed to grow and compound for long periods.

Discounted offers are only available to new members. Stock Advisor will renew at the then current list price. Investing You will end up saving more by investing less money over a longer period of time. Start as early as possible and watch your money work for you. Investing isn't just about how much money you have to invest.

It's also about how much time you have to invest it. That's because of the power of compound growth. Compound interest makes your money grow faster because interest is calculated on the accumulated interest over time as well as on your original principal.

Compounding can create a snowball effect, as the original investments plus the income earned from those investments grow together. As a rule of thumb, to see how long it takes for your savings to double you can use the "Rule of The higher your starting amount and the higher your investment return, the faster your savings compound.

And over time, it can seriously add up. The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest.

Because the interest-on-interest effect can generate increasingly positive returns based on the initial principal amount, compounding has sometimes been referred to as the "miracle of compound interest. Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one.

The total initial amount of the loan is then subtracted from the resulting value. The formula for calculating the amount of compound interest is as follows:. What would be the amount of interest? In this case, it would be:.

Because compound interest includes interest accumulated in previous periods, it grows at an ever-accelerating rate. The interest payable at the end of each year is shown in the table below. Compound interest can significantly boost investment returns over the long term. Interest can be compounded on any given frequency schedule, from daily to annually. There are standard compounding frequency schedules that are usually applied to financial instruments.

The commonly used compounding schedule for savings accounts at banks is daily. For a certificate of deposit CD , typical compounding frequency schedules are daily, monthly, or semiannually; for money market accounts, it's often daily.

For home mortgage loans, home equity loans, personal business loans, or credit card accounts, the most commonly applied compounding schedule is monthly. There can also be variations in the time frame in which the accrued interest is actually credited to the existing balance. Interest on an account may be compounded daily but only credited monthly.

It is only when the interest is actually credited, or added to the existing balance, that it begins to earn additional interest in the account.

Some banks also offer something called continuously compounding interest, which adds interest to the principal at every possible instant. For practical purposes, it doesn't accrue that much more than daily compounding interest unless you want to put money in and take it out the same day. More frequent compounding of interest is beneficial to the investor or creditor. For a borrower, the opposite is true. When calculating compound interest, the number of compounding periods makes a significant difference.

The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest. Compound interest is closely tied to the time value of money and the Rule of 72 , both important concepts in investing. Understanding the time value of money and the exponential growth created by compounding is essential for investors looking to optimize their income and wealth allocation.

The formula for obtaining the future value FV and present value PV are as follows:. The reciprocal of 1. It can only be used for annual compounding. The compound annual growth rate CAGR is used for most financial applications that require the calculation of a single growth rate over a period of time. The CAGR is extensively used to calculate returns over periods of time for stock, mutual funds , and investment portfolios.

The CAGR can also be used to calculate the expected growth rate of investment portfolios over long periods of time, which is useful for purposes such as saving for retirement. Consider the following examples:. Example 2: The CAGR can be used to estimate how much needs to be stowed away to save for a specific objective.

On the positive side, compounding can work to your advantage when it comes to your investments and can be a potent factor in wealth creation.

Exponential growth from compounding interest is also important in mitigating wealth-eroding factors, such as increases in the cost of living, inflation, and reduced purchasing power. Mutual funds offer one of the easiest ways for investors to reap the benefits of compound interest. Opting to reinvest dividends derived from the mutual fund results in purchasing more shares of the fund. More compound interest accumulates over time, and the cycle of purchasing more shares will continue to help the investment in the fund grow in value.

The compound interest is the difference between the cash contributed to an investment and the actual future value of the investment. Of course, earnings from compound interest are taxable, unless the money is in a tax-sheltered account ; it's ordinarily taxed at the standard rate associated with the taxpayer's tax bracket. An investor who opts for a reinvestment plan within a brokerage account is essentially using the power of compounding in whatever they invest.