What Is Compound Interest?
Compound interest can make a significant difference on how you save and invest your money. When you make an initial savings deposit or investment, you begin with a principal sum of money. Depending on the savings or investment vehicle you select, this principal then earns interest, which if you choose to continue to save or reinvest, will earn additional interest. This cumulative earning of interest on interest is referred to as compound interest.
When you leave this interest in your account to continue to grow for a duration of time, you are taking advantage of compound interest. Depending on your interest rate, you can accumulate a significant amount of additional money simply by leaving your initial principal (and any ongoing contributions) alone to earn interest and letting that interest compound year after year, if the period of compounding is annually. Period refers to the frequency in which your principal (and any already earned interest from previous periods) earns additional interest — which could be daily, monthly, semiannually, etc. Compound interest allows an asset to grow at a faster rate than simple interest, which is the money earned only on your principal savings amount.
How Does Compound Interest Work?
Compound interest is calculated according to this mathematical formula:
A = P (1 + r / n)^(nt)
A = the future value of your investment
P = your beginning principal amount (initial deposit)
r = your annual interest rate (as a decimal)
n = the number of times interest is applied (compounded) per time period t
t = the number of time periods your money is invested (duration of your investment)
Let’s consider a specific example. If you begin with an initial deposit amount of $10,000 (P) and invest it in a savings account that earns 3% (r = 0.03) per year with interest that is compounded monthly (n = 12), then after 25 years (t = 25), the future value of your investment would be:
A = P (1 + r / n)^(nt)
A = $10,000 * (1 + 0.03 / 12)^(12 * 25)
= $10,000 * (1.0025)300
= $21,150.20
To calculate simple interest for this example with no compounding, the formula is:
A = P (1 + rt)
= $10,000 (1 + (0.03 * 25))
= $10,000 (1 + 0.75)
= $10,000 (1.75)
= $17,500
Obviously, compound interest can make a big difference when it comes to your wealth accumulation. In this example, compound interest earns you an additional $3,650.20 over the course of 25 years. Are you using the benefits of compounding interest? If not, you could be missing out on some additional long-term earnings that might help you reach your financial goals sooner.
How Do You Get/Earn Compound Interest?
You can earn compound interest by putting your money into various kinds of savings and investment vehicles, such as the following:
- Savings accounts – Regular savings accounts at financial institutions like banks, credit unions and savings and loan institutions generally include compounding interest.
- Certificates of deposit (CDs) – Because you agree to leave your money in CDs for a specified period of time, they generally offer you a higher rate of return than savings accounts and often compound interest on a daily basis, which means a higher effective rate of return. While daily compounding can boost the value of your CD upon maturity, there are usually penalties for early withdrawals, so your money may be inaccessible for longer periods of time.
- Money market accounts – Interest earned on money market accounts is usually compounded daily and deposited monthly. You can take advantage of this compounding by letting your deposits of interest remain in your account to continue to earn additional interest. Money markets generally offer you a higher rate of interest than regular savings accounts.
- Zero-coupon bonds – With a traditional bond, you often receive periodic interest payments in the form of coupons that don’t compound. However, zero-coupon bonds are fixed-income securities that are offered at a deep discount of their original face value. When you invest in a zero-coupon bond, they grow gradually through compounding until you receive principal and interest when it reaches maturity. Like other types of bonds, zero coupon bonds are subject to interest-rate risk if you sell before maturity. If interest rates rise, the value of your zero coupon bond on the secondary market will likely fall. These investments may not keep pace with inflation and default risk should be considered when researching and investing in corporate or municipal zero coupon bonds.
- Stock & mutual fund reinvestments – When you reinvest earnings received from stocks and mutual funds, you can take advantage of compounding. Dividend reinvestment plans allow you to buy additional shares of stocks and mutual funds. By choosing to continually reinvest, you can transform your brokerage account into a compounding one. Keep in mind that all investments come with risk, including the potential for loss of the principal amount invested. Dividends are not guaranteed.
Using This Compound Interest Calculator
Our Compound Interest Calculator estimates the impact of compound interest on the growth of an initial investment amount over time. After inputting your information, the calculator will give you a brief written summary of your results and generate a pie chart to illustrate the value of compound interest. Using different colors, this chart graphically depicts your beginning balance amount, total annual contributions and compound interest earned for the period of time you select. In addition, you can view a detailed data table that summarizes by year your beginning and ending balances, additional savings and compound interest earned.
About Your Inputs
Our Compound Interest Calculator asks you to complete several data fields about the initial amount of your savings and the assumptions you want to make in order to estimate the growth of your investment over time.
Savings
This section asks you about how much money you plan to save or invest:
- Initial balance or deposit – What is the total amount of money you plan to start with?
- Annual savings amount – How much additional money do you plan to save or invest each year and contribute to your account?
Assumptions
This section asks you to make specific assumptions about your saving contributions, duration of time for your investment and rate of return on your money:
- Annual increase in contributions – Indicate the percentage increase (between 0% and 100%) of your yearly savings for this investment. For example, an input of 0% means you will not be making any additional deposits to your initial investment, while an input of 100% means you will contribute twice as much as the previous year.
- Number of years for the analysis – Decide the duration in years (between 1 and 50) for your projected calculations. For example, an input of 25 will calculate the accumulation of compound interest over a period of 25 years.
- Before-tax return on savings – What rate of return do you expect to earn on your investment? You may enter a percentage between -12% (a negative percentage indicates the value of your investment will decrease) and 12% (a positive percentage indicates the value of your investment will increase). Keep in mind this percentage is a before-tax rate of return.
About Your Results
Based on your inputs, this Compound Interest Calculator figures out your cumulative contributions, total accumulation of compound interest and final future account balance of your savings. A pie chart depicts your starting balance, annual contributions and amount of compound interest in different colors.
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