Albert Einstein famously referred to compound interest as the eighth wonder of the world and it’s easy to see why. When it comes to building wealth over time, compound interest is more reliable than trying to pick the next Amazon.com Inc. (NASDAQ: AMZN) or Google Alphabet (NASDAQ: GOOGL). You just have to be a consistent investor and allow the time/value of money to work in your favor.
To calculate compound interest, you need to know a number of variables, such as the principal balance and interest rate. Next, you’ll need to know how much you’ll add to the principal balance and how frequently the interest will compound (the compounding schedule).
If you don't enjoy math, this article is for you. We explain how compound interest is calculated but we’ll also show you how to use the MarketBeat compound interest calculator to make the process easier.
What is Compound Interest?
Compound interest is the interest calculated on a principal balance over a period of time. This includes the current interest on the principal and the interest on all the interest that has accumulated in the previous period.
This is why compound interest is sometimes called “interest on interest” and why Einstein found the concept so fascinating. Compound interest epitomizes the idea of allowing your money to work for you.
The alternative to compound interest is called simple interest. Simple interest is applied at a specific interest rate at a specific moment in time. To illustrate simple interest, we’ll use the example of a bond.
Let’s say you buy a bond that offers a 7% yield at maturity. If the par value (the face value or nominal value) of the bond is $10,000, you will receive $10,700 if you hold the bond to maturity. This amount will not change no matter how long you hold the bond. No compounding would occur.
However, how is compound interest calculated if that same $10,000 were put into an account where that same 7% interest was an annual interest rate that compounded monthly for 12 months? Just 0.58% interest would be applied each month, but the growth including compound interest would look like this:
| End of first month |
$10,058.33 |
| End of second month |
$10,117.01 |
| End of third month |
$10,176.02 |
| End of fourth month |
$10,235.38 |
| End of fifth month |
$10,295.09 |
| End of sixth month |
$10,355.14 |
| End of seventh month |
$10,415.55 |
| End of eighth month |
$10,476.31 |
| End of ninth month |
$10,537.42 |
| End of 10th month |
$10,598.89 |
| End of 11th month |
$10,660.71 |
| End of 12th month |
$10,722.90 |
Assuming you added no more money into the account, you’ll do slightly better holding a bond that accrues compound interest after just one year. The benefits of compounding get significantly better over time.
How to Calculate Compound Interest
To calculate compound interest over time, you’ll need to know the following information:
- Principal balance (starting balance)
- Interest rate
- How frequently compounding takes place
- Length of time invested
For the purposes of the following formulas, we’ll assign variables to each of these data points:
P = Principal
R = Interest rate (as an annual percentage rate)
N = Number of times interest is compounded (per year)
T = Time invested (in years)
To calculate the interest during one compounded period, multiply the principal balance by the interest rate divided by the number of times interest compounds. That looks like this:
P * (R/N)
For example, let’s say you have $10,000 in an account with a 6% annual interest rate, and the interest compounds monthly. At the end of the first month, the value of your account would be the following (assuming nothing was added to the principal):
$10,000 x (0.06 / 12) = $50 in interest
$10,000 + $50 = $10,050.00 as your new account balance
You can calculate compounding interest over longer periods of time. This is easier to do with a financial calculator. Fortunately, you can access free compound interest calculator tools on MarketBeat.
How Compound Interest Grows Over Time
Here are a couple examples to show how compound interest is calculated over time. If you put $10,000 into an account with a 7% APR (annual percentage rate) that compounds monthly for six months, the growth would look like this:
| |
Principal |
Interest |
New Balance |
| End of first month |
$10,000.00 |
$58.33 |
$10,058.33 |
| End of second month |
$10,058.33 |
$58.67 |
$10,117.01 |
| End of third month |
$10,117.01 |
$59.02 |
$10,176.02 |
| End of fourth month |
$10,176.02 |
$59.36 |
$10,235.38 |
| End of fifth month |
$10,235.38 |
$59.71 |
$10,295.09 |
| End of sixth month |
$10,295.09 |
$60.05 |
$10,355.14 |
As you can see, the amount of interest credited to the account each month increases because the interest from previous months has been added to the principal.
Can more frequent compounding offset a lower interest rate? It can seem like it at first. Over time, the higher interest rate is almost always more favorable. Here’s an example that shows what would happen to $8,000 over one year if the money were placed in a product with a 5% APR compounding monthly versus one with a 6% APR that compounds every six months.
| |
Product 1 (5% APR, compounding monthly) |
Product 2 (6% APR, compounding every six months) |
| Month 1 |
$8,033.33 |
$8,000.00 |
| Month 2 |
$8,066.81 |
$8,000.00 |
| Month 3 |
$8,100.42 |
$8,000.00 |
| Month 4 |
$8,134.17 |
$8,000.00 |
| Month 5 |
$8,168.06 |
$8,000.00 |
| Month 6 |
$8,202.09 |
$8,240.00 |
| Month 7 |
$8,236.27 |
$8,240.00 |
| Month 8 |
$8,270.59 |
$8,240.00 |
| Month 9 |
$8,305.05 |
$8,240.00 |
| Month 10 |
$8,339.65 |
$8,240.00 |
| Month 11 |
$8,374.40 |
$8,240.00 |
| Month 12 |
$8,409.30 |
$8,487.20 |
As you can see, by the sixth month, the account that compounded monthly already lagged behind the account that had the 1% better interest rate. However, with a small enough difference in interest rate and enough time to compound, a faster compounding schedule can come out ahead. For example, if you had 5 years and $12,000, investing it at a 5% APR with monthly compounding would make you $12 richer than investing it at a 5.1% APR with annual compounding.
How to Use the Compound Interest Calculator
Compound interest can offer you a tremendous opportunity to build wealth over time. However, maximizing this benefit requires discipline and time. One of the problems with maintaining that discipline is understanding how to calculate interest compounded over time.
MarketBeat’s easy-to-use tool can show you how contributing specific amounts over specific time periods will grow using different compounding schedules.
Here’s a step-by-step guide to the MarketBeat compound interest calculator.
Step 1: Enter your initial principal balance.
If you’re buying a bond, this will be the par value (or face value) of the bond (such as $5,000). If you’re checking up on a savings account, enter the amount of your initial deposit. This is not an ideal tool for stocks because of the frequency with which the principal value can change.
For that, you may want to use the MarketBeat stock profit calculator.
Step 2: Enter the amount you will contribute and the frequency.
For bonds, you will leave this blank because buying a bond is a one-time event. In the case of a savings account, you’ll need to consider how different dollar amounts and the frequency that you add to them changes the compounding effect.
For example, what would happen to $8,000 over one year if you placed it in a product with a 5% APR and that compounded monthly, or one with a 10% APR that compounded at every six months? How would that change if you added an additional $1,000 monthly or $10,000 annually? You can play around with the calculator to find out.
Step 3: Enter compounding time.
The benefit you get from compounding interest will increase over time. The longer you have to let your money work for you, the better. In this step, you’ll enter the amount of time in days, weeks, months, quarters or years that the money will stay in the investment.
Step 4: Enter the compounding type (or schedule).
The most common types of compound interest include daily, monthly or annual compounding, also referred to as compound interest schedules. In this step, you can see how the calculation changes on different schedules.
Step 5: Enter the withdrawal amount and frequency.
If you’re an investor on a fixed income, you’ll likely take regular withdrawals from your account. To calculate compound interest with complete accuracy, enter the amount you will withdraw from the account and at what frequency. If you don’t plan to make withdrawals from the account, just leave this at zero.
Step 6: Enter the interest rate.
This is the interest rate for the bond or interest-bearing account. To ensure accuracy when calculating compound interest rate, include the exact interest rate (such as 5.25% instead of 5%). Even a small difference in interest rate can make a big difference over time.
If you’re interested in other calculators like this, check out the MarketBeat retirement calculator, the MarketBeat stock average calculator and for options traders, the MarketBeat options profit calculator.
How to Make Compound Interest Work for You
The benefits of compounding for investors come primarily through regular and systematic principal growth. 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 allow the time value of money to work for you.
Most of our investments do not pay us compound interest. If you’re a bond holder with a 5% yield on a bond, you will receive 5% above your principal at the maturity date. Likewise, if you’re entitled to receive a quarterly dividend of 4% on another stock, you’ll receive that dividend based on the market value of you're account at that time.
Can Compound Interest Make You Rich?
Yes, because compound interest makes a dollar today worth more than a dollar earned a month from now. It’s why most experts encourage investors to start saving as early as possible. It will take less capital on a monthly or yearly basis to accomplish your goals when you start earlier.
Many financial professionals illustrate the power of compound interest using the “Rule of 72,” which shows clients how soon they can double their money assuming a particular interest rate. The Rule of 72 is a simplified equation; the interest rate is divided by the number 72 to get the number of years it would take to double an investment. This rule is based on an annual compounding schedule.
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 employee-sponsored account. Not only do you reduce your tax burden, you maximize the advantages of compounding your money.
Examples of Compound Interest Calculations
Here are two examples that show how compound interest is calculated with different variables.
Annual Compound Interest
In this example, we’ll assume that an individual makes an initial investment of $8,000. The investment compounds annually at an interest rate of 5%. The formula looks like this:
A = P(1 + r/n)nt
A = 8,000.00(1 + 0.05/1)(1)(3)
A = 8,000.00(1 + 0.05)(3)
A = $9,261.00
Monthly Compound Interest
In this example, we’ll assume the same initial investment of $8,000. But this time the investment compounds monthly at an interest rate of 3% for a period of three years. The formula looks like this:
A = P(1 + r/n)nt
A = 8,000.00(1 + 0.03/12)(12)(3)
A = 8,000.00(1 + 0.0025)(36)
A = $8,752.41
The MarketBeat compound interest calculator does the math for you to help you determine the best scenario for you to grow wealth over time.
Compound Interest Schedules
In theory, you can calculate compound interest as frequently as you may want to calculate it (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 typically compounds daily, whereas a certificate of deposit (CD) might compound daily, monthly or semi-annually. For loans such as mortgages and credit cards, compound interest normally calculates monthly.
Pros and Cons of Compound Interest
Compound interest is truly one of the most risk-free ways to build wealth. When you have investments that generate a regular interest rate, you have the benefit of allowing that interest to compound over time. If you make regular contributions to the principal balance, the compounding effect will be even greater.
Pros
When you are the investor (or the person to whom the interest is owed), more frequent compounding is a benefit. One of the key benefits of compound interest is that it can allow your investments to outpace the effect of factors that can erode wealth, such as inflation.
Cons
If you are the borrower (or the person who has to pay the interest) you would want less frequent compounding.
When you take out a loan, compounding interest can be your enemy or your friend. If you can afford to pay back the loan immediately or if you plan to pay significantly more than the required minimum every month, then you will reduce your interest payments if they are calculated using a compound interest schedule, as opposed to simple interest.
For example, if you have a $5,000 loan with 5% annual percentage rate (5%), you would be charged 5% of the principal balance for every month you have the loan. In the first month, your interest payment would be approximately $21. As you pay down the principal, the interest would go down because the principal would be lower. For a simple interest loan, the interest payment will remain the same, no matter the principal balance.
Make Compound Interest Work for You
Compound interest includes the current interest on the principal as well as the interest on all the interest that has accumulated in the time between compounding. The benefits of compounding for investors come primarily through regular and systematic growth in the principal balance.
It’s important to understand that time truly is your biggest ally. A dollar that you invest today will be worth significantly more down the road than a dollar invested a month or a year from now.
FAQs
Let’s take a look at a few frequently asked questions about compound interest.
What is compounding interest?
Compound interest is the interest that is calculated on a principal balance over a period of time. This includes not only the current interest on the principal, but also the interest on all the interest that has accumulated in the previous period.
What are the three types of compound interest?
In theory, interest can be calculated as frequently as someone would want to calculate it (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.
How do you calculate compounding interest?
To calculate compound interest you need to know your starting principal balance, how much money you plan to add to that principal and on what schedule, how frequently interest will be paid and your interest rate. You can also include how much and at what frequency you plan to take money from the account.
