How compound interest works
Compound interest is the force that turns modest savings into substantial wealth over time. Key differences from simple interest:
- Earns on principal and interest — Unlike simple interest (which only calculates returns on your initial principal), compound interest earns returns on both your principal and all previously earned interest.
- Exponential growth — Each compounding period, your interest is added to your balance, and the next period's interest is calculated on that larger base. Your money grows faster and faster as interest compounds on interest.
- Time is the multiplier — The longer you compound, the more dramatic the effect. Starting early and giving your money time to grow is the key to wealth-building.
Worked example
$10,000 invested at 7% annual interest compounded monthly:
- No contributions — Grows to about $40,000 in 20 years
- With $200/month contributions — Balloons to over $132,000 in 20 years, earning you over $74,000 in pure interest
The compound interest formula
Where:
- A — Final amount (future value)
- P — Principal (starting amount)
- r — Annual interest rate (as a decimal)
- n — Compounding frequency per year
- t — Time in years
- PMT — Periodic contribution amount
The power of monthly contributions
Regular contributions magnify compound interest. Even if you start with a small principal, adding money every month creates dozens of mini-investments that all compound independently.
| Scenario | Total Contributed | Final Balance (20 yrs, 7%) | Interest Earned |
|---|---|---|---|
| $10,000 initial only | $10,000 | $40,000 | $30,000 |
| $10,000 + $200/month | $58,000 | $132,683 | $74,683 |
The earlier contributions have the most time to compound, so front-loading your savings whenever possible maximizes the effect. Our Savings Goal Calculator flips this formula around: tell it your target amount and deadline, and it will calculate the monthly contribution you need to hit that goal.
Compounding frequency: daily vs. monthly vs. annual
The frequency of compounding has a small but real impact on your final total:
- Daily compounding — 365 periods per year, earns slightly more
- Monthly compounding — 12 periods per year, most common for savings accounts
- Annual compounding — 1 period per year, typical for bonds and CDs
The difference is modest over a few years but grows over decades. Most high-yield savings accounts and money market accounts compound daily. If you are comparing two accounts with the same nominal rate, the one that compounds more often will give you a higher effective return.
Future value vs. present value
This calculator computes future value — what your money will be worth at a future date given a certain interest rate and contribution schedule. Related calculators:
- Future Value Calculator — Lump-sum projections without contributions
- Present Value Calculator — How much you need to invest today to reach a specific future amount
Estimating realistic rates of return
The interest rate you enter determines everything. Typical ranges:
- Stock portfolios (diversified) — About 10% annually before inflation, or roughly 7% after inflation (historically)
- Conservative bond portfolios — 4-5%
- High-yield savings accounts — 4-5% (fluctuates with Federal Reserve policy)
- CDs and Treasury bonds — Guaranteed rate for a fixed term, currently 3-5%
No return is guaranteed, and past performance does not predict future results. Use this calculator to model different scenarios, not as a promise of what you will actually earn.
Using this calculator for retirement planning
- Enter your current balance as the principal
- Set the expected annual return (often 6-8% for diversified portfolios)
- Enter your planned monthly or annual contribution
- Adjust for inflation — These calculators show nominal dollars (future year dollars, which will be worth less due to inflation). Either use a lower "real" return (subtract 2-3% for inflation) or plan to have more than the calculator says.
Our CAGR Calculator can help you measure the actual historical return of your portfolio over time.
Tax considerations
This calculator does not account for taxes. Key points:
- Tax-advantaged accounts (401k, IRA) — Money compounds tax-deferred (traditional) or tax-free (Roth)
- Taxable accounts — You may owe taxes on interest, dividends, and capital gains each year, which reduces your effective return. If you are modeling a taxable account, use a lower after-tax rate.
Example: If you expect 7% but pay 25% in taxes on your gains, your effective rate is closer to 5.25%.