Compound Interest Calculator

Compound interest is the formal name for the snowball effect in finance, where an initial amount grows upon itself and gains more and more momentum over time. It is a powerful tool that can work in your favor when saving, or prolong repayment for debts. Compound interest is often referred to as “interest on interest” because interest accrued is reinvested or compounded along with your principal balance. It is the interest earned on both the initial sum combined with interest earned on already accrued returns.

When saving and investing, this means that your wealth grows by earning investment returns on your initial balance and then reinvesting the returns. However, when you have debt, compound interest can work against you. The amount due increases as the interest grows on top of both the initial amount borrowed and accrued interest.

Compound interest is often calculated on investments such as retirement and education savings, along with money owed, like credit card debt. Interest rates on credit card and other debts tend to be high, which means that the amount owed can compound quickly. It's important to understand how compound interest works so you can find a balance between paying down debt and investing money.

Simple Interest vs. Compound Interest

Simple interest is when interest is gained only on the principal amount. In this scenario, interest earned is not reinvested. If you were to gain 10% annual interest on $100, for example, the total amount earned per year would be $10. At the end of the year, you’d have $110: the initial $100, plus $10 of interest. After two years, you’d have $120. After 20 years, you’d have $300.

Compound interest, on the other hand, puts that $10 in interest to work to continue to earn more money. During the second year, instead of earning interest on just the principal of $100, you’d earn interest on $110, meaning that your balance after two years is $121. While this is a small difference initially, it can add up significantly when compounded over time. After 20 years, the investment will have grown to $673 instead of $300 through simple interest.

You can use compound interest to save money faster, but if you have compound interest on your debts, you’ll lose money more quickly, too. Interest may compound on a daily, monthly, annual or continuous schedule. The more frequently the sum is compounded, the faster it will grow.

How Compound Interest Works

Compound interest allows investments to work in your favor. The earlier you start saving money, the better. But the longer you take to pay off your compound interest debts, the higher they will become.

Compound interest is often compared to a snowball that grows over time. Much like a snowball at the top of a hill, compound interest grows your balances a small amount at first. Like the snowball rolling down the hill, as your wealth grows, it picks up momentum growing by a larger amount each period. The longer the amount of time, or the steeper the hill, the larger the snowball or sum of money will grow.

In terms of debt, compound interest can be like a pest problem. Let’s say you find two bed bugs in your room. You could get rid of them now, but instead, you wait a few days to take care of them. Then you discover that there are now dozens of bed bugs in your room. If you had taken care of the bed bugs right away, they wouldn’t have been able to multiply at such a rate.

With compound interest investments, it’s better to wait and allow these investments to grow, but with money you owe, it’s usually best to pay down debt as quickly as possible — especially if your interest rate is high.

How Does Compound Interest Grow Over Time?

Compound interest can grow exponentially over time. For example, let’s say you invest $500 at an 8% annual return. Over five years, this is how much cumulative interest you will earn if the interest is compounded monthly:

• Year one: $42
• Year two: $86
• Year three: $135
• Year four: $188
• Year five: $245

How to Calculate Compound Interest

With the compound interest formula, you can determine how much interest you will accrue on the initial investment or debt. You only need to know how much your principal balance is, the interest rate, the number of times your interest will be compounded over each time period, and the total number of time periods.

Applying the Formula for Compound Interest

The compound interest formula is:

where:

• P is the initial principal balance
• r is the interest rate (typically, this is an annual rate)
• n is the number of times interest compounds during each time period
• t is the number of time periods
• A is the ending balance, including the compounded interest

To calculate only the compound interest portion (CI), the above formula can be modified by subtracting the initial principal (P):

where:

• CI is the compound interest earned

To calculate the ending balance with ongoing contributions (c), we add a term that calculates the value of ongoing contributions to the principal balance.

Where:

• c is the amount of the periodic contribution

MoneyGeek’s Compound Interest Calculation

MoneyGeek’s compound interest calculator calculates compound interest using the above formulas. If you have selected monthly contributions in the calculator, the calculator utilizes monthly compounding, even if the monthly contribution is set to zero. If the contribution frequency is annual, annual compounding is utilized, again if the annual contribution is set to zero.

The MoneyGeek compound interest calculator is simple to use and understand. Instead of using the compound interest formula, all you have to do is plug in your numbers and information about the interest. You can utilize this tool to determine how much you will owe in interest on your debt or estimate how much you will earn in interest on your investments.

Enter Your Initial Amount

Start by entering the principal amount of your debt or investment. If you’re investing $500, for example, type that number in the box.

Set Monthly or Annual Contributions

This is how much you’re going to contribute to your investment or pay off your debt. For instance, if you’re investing an additional $20 a year, enter that figure into the calculator and select “Annually.” If you plan to pay $20 toward your debt each month, add that number and select “Monthly.” Try changing the dollar amounts up or down to see what happens to the ending balances.

Estimate Your Rate of Return

This is where you enter how much compound interest you expect to receive on an investment or pay on a debt. If you have an 8% interest rate, you will enter that here. The rate of return on many investments is speculative, so entering an average number can give you an idea of how much you’ll earn over time. The rate of return you earn on your investments can make a big difference. See what the change in your balance is if you increase or decrease your rate of return by 1 or 2 percentage points.

Set the Number of Years of Growth

Enter the number of years you plan to keep your money in an investment or how long you will take to pay off your debt. For example, let’s say you won’t touch your investment for five years, so enter five in that box. Try doubling your investment period: How much would you earn if you held it twice as long?

Use the Bar Chart to Explore Growth Over Time

With the compound interest calculator, you can switch the view to see a comprehensive breakdown in different formats. The initial bar chart showcases how compound interest grows over time on top of your principal amount.

Examine the Totals by Source Pie Chart

The MoneyGeek compound interest calculator uses a pie chart to show you the initial amount you contributed in purple, the total interest you earned in green and your total contributions in blue.

Review the Table View

Just click the compound interest table on the right, and you’ll see each year, your starting balance, your annual contributions, cumulative contributions, interest earned, cumulative interest and total balance. You can even see how much you’d earn if you kept saving at that rate, or how much you’d be charged in compound interest if you wanted to pay off your debt.