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.
