If you’ve ever borrowed money or tried your hand at investing, chances are you’ve heard the term, compound interest, a few times. But what does it mean, and how does it work? Do you simply take the rate and multiply it by the principal to find the figure you’re looking for? Or is there much more to the equation?
Read on to learn the answer to these questions and much more.
A Closer Look at How Compound Interest Works
Unlike simple interest that is derived from the principal, compounding interest actually allows you to earn interest on top of interest until you withdraw funds. On the other hand, it can work against you when borrowing money as you’ll be on the hook for the additional interest accrued over time.
A few key benefits of compound interest investment products:
- Your money can grow exponentially even if you choose not to make additional contributions
- Deposit or investment products that compound frequently (i.e. daily versus monthly) can help you earn even more money faster
How to Calculate Compound Interest
In order to fully understand how compound interest works, you must start with simple interest. If you need a refresher, you can view this comprehensive guide to bring you up to speed. (hyperlink to simple interest post)
The Compound Interest Formula
To compute compound interest, use the formula listed below. There’s also a legend of what each input means for your reference.
A = P ( 1 + [ r / n ] ) ^ nt
Inputs:
- A- final amount after compound interest is computed
- p- principal
- r- annual interest rate
- n- number of compounding periods per year
- t- time in years money compounds
Scenario #1: Daily Compounding
To start building an emergency fund, you open an account that compounds interest daily with a deposit of $4,000. With an interest rate of 3 percent, how much will you accumulate by the end of the first year?
The formula: A = P ( 1 + [ r / n ] ) ^ nt
Step 1: A = $4,000 ( 1 + [.03 / 365 ] ) ^ (365*1)
Step 2: A = $4,000 (1.00008) ^ 365
Step 3: A = $4,000 (1.03045)
Step 4: A = $4,121.81
Scenario #2: Monthly Compounding
Assume you invest $2,000 in a five-year Certificate of Deposit (CD). Your financial institution will pay you a rate of 6 percent, compounded monthly, for the duration of the CD term. Here’s how to determine how much you’ll earn in interest:
The formula: A = P ( 1 + [ r / n ] ) ^ nt
Step 1: A = $2,000 ( 1 + [.06 / 12 ] ) ^ (12*5)
Step 2: A = $2,000 (1.0005) ^ (60)
Step 3: A = $2,000 (1.3489)
Step 4: A = $2,697.70
Your CD will be worth $2,697.70 at the conclusion of five years, and you’ll earn $697.70 in interest.
Scenario #3: Annual Compounding
You take out a seven-year loan of $15,000 with an interest rate of 9 percent that compounds annually. The calculation below shows how much you’ll pay in interest over the life of the loan, and in interest.
The formula: A = P ( 1 + [ r / n ] ) ^ nt
Step 1: A = $15,000 ( 1 + [.09 / 1 ] ) ^ (1*7)
Step 2: A = $15,000 (1.09) ^ (7)
Step 3: A = $15,000 (1.82804)
Step 4: $27,420.59
You’ll pay $27,420.59 over the life of the loan, or $12,420.59 in interest.
The Bottom Line
While it won’t necessarily work in your favor when repaying loans, compound interest is ideal if you’re looking to grow your money fast. But if the thought of computing compound interest by hand scares you, there are several online calculators you can use to do the legwork.
