See exactly how your savings and investments will grow over time with the power of compound interest.
Compound interest is one of the most powerful concepts in personal finance. Unlike simple interest, which is only calculated on your original deposit, compound interest earns returns on both your principal and your previously accumulated interest. Over long periods of time, this creates an exponential growth curve that Albert Einstein allegedly called "the eighth wonder of the world."
The formula for compound interest is:
Where A is the final amount, P is your initial principal (starting deposit), r is the annual interest rate expressed as a decimal, n is the number of times interest compounds per year, and t is the number of years your money is invested.
For example, if you invest $10,000 at a 7% annual rate compounded monthly for 20 years, your investment would grow to approximately $40,387. That means you earned over $30,000 in interest on a $10,000 deposit. Add monthly contributions to the equation and the numbers become even more dramatic.
At its core, compound interest means earning interest on your interest. Imagine you deposit $1,000 in a savings account that pays 5% annually. After year one, you have $1,050. In year two, you earn 5% on $1,050 (not just the original $1,000), giving you $1,102.50. Each year, the base amount grows, and your earnings accelerate.
This is why starting early matters so much. An investor who begins at age 25 and contributes $200/month at 7% will have significantly more at retirement than someone who starts at 35 with the exact same contributions. Time is the single most important variable in the compound interest equation.
Simple interest only calculates returns on the original principal. If you invest $10,000 at 7% simple interest for 20 years, you earn $14,000 in interest for a total of $24,000. With compound interest at the same rate compounded monthly, you end up with over $40,000. The difference is over $16,000, and it only grows wider with longer time horizons.
The more frequently interest compounds, the more you earn. Annual compounding applies interest once a year. Monthly compounding applies it twelve times a year, and daily compounding applies it 365 times. In practice, the difference between daily and monthly compounding is small (often just a few dollars per year on moderate balances), but the jump from annual to monthly compounding is meaningful. Most savings accounts and investment vehicles compound daily or monthly.
Compound interest is not limited to bank accounts and investments. It shows up everywhere in personal finance. Mortgage payments involve compounding, which is why a 30-year mortgage on a $300,000 home at 7% costs over $418,000 in interest alone. Student loan interest compounds, which is why balances can grow even while making payments if the payments do not cover the monthly interest. Reinvested dividends in index funds compound over decades, which is how ordinary people build wealth through consistent investing.
One of the most counterintuitive facts about compound interest is that starting early often beats starting with more money. Consider two investors: Investor A starts at age 22, invests $300/month for 10 years, then stops entirely. Investor B waits until age 32 and invests $300/month continuously until age 62. Despite investing for 30 years compared to just 10, Investor B ends up with less money than Investor A, assuming the same 8% return. Investor A's 10 extra years of compounding on the early contributions outweigh 20 additional years of contributions. This is a powerful argument for starting as early as possible, even with small amounts.
Investment fees compound just like returns do, except they work against you. A seemingly small difference of 1% in annual fees can cost you hundreds of thousands of dollars over a career. On a $500/month investment over 30 years at 8%, a fund with 0.1% fees yields about $707,000 while a fund with 1.1% fees yields about $582,000. That 1% fee difference cost $125,000. This is why low-cost index funds have become so popular for long-term investors.
For a deeper look at how $100/month can grow into a million dollars, read our guide on Compound Interest Explained. To see how compound growth applies to retirement planning specifically, try the Retirement Calculator or read Retirement Savings by Age. For those pursuing early financial independence, the FIRE Calculator uses these same principles to estimate your timeline.