Explore the magic of compound interest.
Compound interest is the most powerful tool in the world of personal finance. The magic of compound interest occurs when you invest money, earn interest on your initial investment, and then earn interest on the interest you previously accumulated. Use high yield savings accounts (HYSAs) and retirement investment accounts like IRAs and 401(k)s to take advantage of earning compound interest. Also learn how interest rates affect the total amount of interest you pay on debt over time like mortgages and student loans. The compound interest calculator and chart below show how you can benefit from the magic of compound interest over time.
What is compound interest?
When you think of compound interest, think of a snowball rolling down a hill. The ball starts small, but as it rolls down the hill and collects more snow, the snowball grows larger. Similarly, when you add money to a savings, investment, or retirement account, your account balance starts off small, like the snowball at the top of the hill. As time goes on (and the snowball rolls down the hill), you accumulate interest, and the account total (size of the snowball) grows. As the balance of the account keeps growing, it ends up growing faster because you make additional interest on the interest you previously earned.
Let's look at an example with numbers. Angie is 22 years old and just started her first job out of college. She opens a Roth IRA account and puts $1,000 in it right away. Each month, she adds $100 to the account and invests in an S&P 500 index fund. After 20 years, assuming the S&P 500 grows 7% a year on average, Angie will have over $56,000 in her account! She will have contributed $25,000 of her own money, but have earned over $31,000 in interest! Compound interest now makes up the majority of the balance in Angie's investment account. That's the magical power of compounding for you!
The math
If you're interested in the math, use the following compound interest formula:
$$\textbf{A} = P(1 + \frac{r}{n})^{nt}$$
Where:
- A: Total balance (interest + initial investment + deposits)
- P: Principal (initial investment)
- r: Annual interest rate (as a decimal)
- n: Number of compounding periods (n=12 in the chart and example above)
- t: Time in years (as a decimal or fraction if there is a partial year)
Next, we can find the total amount of interest earned using this equation:
$$\textbf{Total Interest Earned} = A - P$$