What to enter
- Starting balance
- The amount you have at the beginning. It can be zero if you are starting with monthly deposits only.
- Monthly contribution
- The amount you add every month. Contributions are what make ordinary savers’ balances grow; the calculator lets you test how much they matter.
- Annual interest rate
- The stated (nominal) yearly rate before compounding. If you only have a yield figure, such as an APY, see the note in the results section.
- Compounding frequency
- How often interest is added to the balance: annually, semiannually, quarterly, monthly or daily. More frequent compounding produces slightly more.
- Years to grow
- The length of time you leave the money invested or saved, from 1 to 80 years.
- Contributions are made
- At the end of each month (the default) or at the start. Deposits at the start earn one extra month of interest.
How to read your results
The headline is the final balance. The table separates what you put in from what growth added: total contributed (starting balance plus every deposit) and interest earned. The effective annual yield (APY) converts your stated rate and compounding frequency into the yield you would actually earn in a year, which allows a fair comparison between accounts that compound differently. A lump sum doubles in about shows how long a single deposit takes to double at that yield. When interest earned first exceeds everything you have contributed, the table notes the year, which is the point where compounding starts to do more work than you do.
The stacked chart shows contributions and growth over time, and the table underneath gives the balance year by year, so you can see how growth accelerates in the later years.
The formulas
Interest compounds when it is added to the balance and then earns interest itself. For a single amount, the value after t years is:
The effective annual yield is the same growth measured over one year:
With regular monthly contributions, the calculator converts the stated rate into an equivalent monthly rate, (1 + r ÷ n)n ÷ 12 − 1, and steps through the schedule month by month: interest is added to the balance, and the contribution is added at the end (or start) of the month. Stepping month by month avoids the need for a separate annuity formula and works for any compounding frequency.
The doubling time shown is exact for the yield: ln 2 ÷ ln (1 + APY). The familiar rule of 72, which divides 72 by the percentage rate, is a quick approximation of the same thing.
Worked example
$5,000 start, $200 a month, 7% for 20 years
With monthly compounding, the balance after 20 years is $124,379. You contributed $53,000 in total ($5,000 plus 240 deposits of $200), so $71,379 of the balance is interest. The APY is 7.229%, and a lump sum at this yield doubles in about 9.9 years. Interest first exceeds total contributions in year 17.
Compounding frequency matters little. Compounded annually the same inputs give $120,856, and compounded daily they give $124,709. The gap between the two is $3,854 over 20 years, which is small next to the effect of time or contributions.
Time matters a lot. Ten years gives $44,665, twenty gives $124,379 and thirty gives $284,577. The last ten years add more than the first twenty combined. Contributions matter too: raising the deposit from $200 to $300 lifts the 20-year balance to $176,472. And depositing at the start of each month instead of the end adds $608.
A single deposit. $10,000 with no further contributions at 6% for 12 years grows to $20,508.
Nominal rate, APY and comparing accounts
Banks and brokers describe growth in two ways. The interest rate (nominal rate) is the stated yearly rate before compounding. The APY (annual percentage yield) includes the effect of compounding and is what you actually earn over a year. A 5% rate compounded monthly has an APY of about 5.12%. When you compare savings accounts or certificates of deposit, compare APYs. When you enter a figure into this calculator, use the nominal rate together with the matching compounding frequency. If you only have an APY and want the exact result, select annual compounding and enter the APY as the rate, which gives the same growth over a year.
Loans compound in the same way, but against you. Credit card balances that compound daily at a high rate grow quickly when unpaid, which is why the debt payoff calculator is worth using alongside this one.
What the projection leaves out
The projection uses one constant rate. Savings account rates change, and investment returns vary from year to year, sometimes widely, so treat the result as an illustration rather than a forecast. It is also a pre-tax and pre-fee figure: taxes on interest, account fees and investment expenses lower real growth, and inflation reduces what the future balance will buy. To see the effect of fees and inflation on an investment projection, use the investment return calculator, and to see inflation over specific years, the inflation calculator. If your goal is a target amount, the savings calculator solves for the time or the deposit you need.
Frequently asked questions
What is compound interest?
Compound interest is interest calculated on both the original balance and the interest already added. Because each period’s interest becomes part of the base for the next, growth accelerates over time.
Does more frequent compounding make a big difference?
Usually not a large one. The example shows daily compounding beating annual compounding by a small amount over 20 years. The rate, the time and the size of contributions matter far more.
What is the rule of 72?
It is a shortcut: divide 72 by the annual percentage return to estimate how many years it takes money to double. At 7% it gives about 10.3 years. The calculator shows an exact figure.
Should I enter APY or the interest rate?
Enter the nominal interest rate with its compounding frequency for the exact result. If you only know the APY, choose annual compounding and enter the APY as the rate.
Does this account for taxes, fees or inflation?
No. It shows growth before taxes, fees and inflation. Those reduce real returns.
Are these numbers guaranteed?
No. They are a projection based on the constant rate you enter. Actual returns vary.