Compound Interest Calculator
Growth with interest on interest — principal, rate, time, compounding frequency, and optional monthly deposits.
Updated
Added each compounding period. Leave at 0 for none.
Final balance
$1,647.01balance
after 10 years
- Starting principal
- $1,000.00
- Total deposits
- $0.00
- Interest earned
- $647.01
- Final balance
- $1,647.01
Estimates for general information, not financial advice.
In short
How do you calculate compound interest?
Balance = P × (1 + r ÷ n)^(n × t), where n is how many times a year the interest compounds. Run $1,000.00 at 5% for 10 years compounded monthly and n = 12, so the balance is 1000 × (1 + 0.05 ÷ 12)^120 = $1,647.01, of which $647.01 is interest. Compounded once a year instead it reaches only $1,628.89.
Frequency matters far less than people expect: going from annual to monthly adds $18.11 here, while going from daily all the way to continuous adds six cents.
How to use the compound interest calculator
Enter your starting principal, the annual interest rate as a percent, and the number of years the money has to grow. Pick a compounding frequency, monthly by default, or daily, quarterly, or annually, and add a monthly contribution if you plan to keep saving.
The calculator returns the ending balance, the total you deposited, and the interest earned on top, and every result updates the moment an input changes. The rate you type is an assumption you are making, not a rate anyone is offering you, so it is worth running two or three rates to see how sensitive the answer is.
$1,647.01
Ending balance
$1,000 at 5% for 10 years, monthly
$647.01
Interest earned
growth on the original $1,000
×1.647
Growth factor
(1 + 0.05 ÷ 12) raised 120 times
The years input doubles as a slider you can drag from 1 to 50, which is the fastest way to see compounding in action. Slide the term out and watch the balance curve upward rather than climb in a straight line.
Early on the gains look modest, because each year the interest is calculated on a balance that already includes every previous year of interest, and it takes a while for that to amount to much. Then the line bends steeper, and the later years of a long term do far more work than the early ones ever did.
Need the flatter case instead?
Simple interest never pays interest on interest, so the balance climbs in a straight line. That is the right tool for a fixed-term note or any loan quoted that way.
Open the simple interest calculator →To model steady saving, add a monthly contribution, and that is where the balance really moves. Each deposit gets its own stretch of compounding, so the earliest deposits do the most work, and the contributions and the growth on them reinforce one another over the full term.
The balance of deposits versus growth shifts toward growth as the horizon lengthens, which is the real argument for starting early rather than saving harder later. The total-deposits figure is always broken out separately, so you can see exactly how much of the result you supplied yourself.
- Starting principal
- $1,000.00
- Monthly deposit, 120 months
- $12,000.00
- Rate and frequency
- 5%, compounded monthly
- Interest earned
- $4,175.24
- Ending balance
- $17,175.24
About a quarter of the ending balance is growth; the rest is the discipline of depositing.
Do
- Enter the nominal annual rate and let the tool divide it by the compounding frequency.
- Run two or three rates, because the rate you type is an assumption rather than an offer.
- Read the total deposits and the interest separately before judging whether the return did much work.
- Compare two accounts by APY, the single figure that folds rate and frequency together.
Don't
- Divide the annual rate by twelve yourself before entering it, or the growth is applied twice over.
- Chase a higher compounding frequency, since monthly already captures more than 90 percent of the effect.
- Treat the projected balance as a promise; it is arithmetic performed on a rate you supplied.
- Assume a contribution starts earning the day you make it, as each one lands at the end of its period.
The compounding-frequency ladder, all on the same $1,000.00 at 5% for 10 years. The point of the table is the fourth column: the gain over annual compounding rises steeply at first and then flattens almost completely, so the last several steps are worth pennies.
| Compounding frequency | Periods per year | Balance after 10 years | Gain over annual compounding | Effective annual yield (APY) |
|---|---|---|---|---|
| Annually | 1 | $1,628.89 | baseline | 5.0000% |
| Semiannually | 2 | $1,638.62 | +$9.72 | 5.0625% |
| Every four months | 3 | $1,641.94 | +$13.05 | 5.0838% |
| Quarterly | 4 | $1,643.62 | +$14.72 | 5.0945% |
| Every two months | 6 | $1,645.31 | +$16.41 | 5.1053% |
| Monthly | 12 | $1,647.01 | +$18.11 | 5.1162% |
| Semimonthly | 24 | $1,647.86 | +$18.97 | 5.1216% |
| Biweekly | 26 | $1,647.93 | +$19.04 | 5.1221% |
| Weekly | 52 | $1,648.33 | +$19.43 | 5.1246% |
| Daily, 360-day year | 360 | $1,648.66 | +$19.77 | 5.1267% |
| Daily, 365-day year | 365 | $1,648.66 | +$19.77 | 5.1267% |
| Hourly | 8,760 | $1,648.72 | +$19.82 | 5.1271% |
| Continuous | unbounded | $1,648.72 | +$19.83 | 5.1271% |
Does compounding frequency actually matter?
Less than most people assume, and the effect flattens fast. At the same 5% rate over 10 years, $1,000.00 grows to $1,628.89 compounded annually, $1,643.62 quarterly, $1,647.01 monthly, and $1,648.66 daily. The chart below shows what each step up the ladder is actually worth, and the reference table above lays out the whole ladder from annual to continuous, with the APY each schedule works out to.
Read it: More than 90 percent of everything frequency can give is already captured at monthly, and the leap from daily to continuous, the theoretical ceiling, is worth six cents.
Computed from balance = P × (1 + r ÷ n)^(n × t); continuous uses P × e^(r × t).
Full guide
How Does Compound Interest Work? The Math That Grows Money
Interest that earns interest — the formula, the frequency gap, and why steady deposits and time do most of the work.
Read the full guide →The formula, worked line by line
Compound interest pays interest on your interest. Each period the balance is multiplied by a small growth factor, 1 + r ÷ n, and because that factor applies to a balance that already includes every past period of interest, the total accelerates instead of climbing in equal steps. The rate that goes into the factor is the periodic rate, the annual rate divided by the number of compounds per year, and the exponent counts periods rather than years.
A recurring deposit is handled separately, as an ordinary annuity. Each contribution lands at the end of its period and then compounds for however many periods remain, so the earliest deposit does the most work and the final one earns nothing at all. Adding the two pieces together gives the full balance.
n = compounds per year (12 monthly, 365 daily, 4 quarterly, 1 annually)
balance = P × (1 + r/n)^(n × years)
with deposits: + PMT × [ ((1 + r/n)^(n × years) − 1) ÷ (r/n) ]
interest = balance − principal − total deposits- Principal
- P = $1,000.00
- Periodic rate
- 0.05 ÷ 12 = 0.0041667
- Periods
- 12 × 10 = 120
- Growth factor
- (1.0041667)^120 = 1.64701
- Ending balance
- $1,647.01
Interest = $647.01. The same money compounded annually reaches $1,628.89, because it compounds 10 times instead of 120. Add a $100.00 monthly deposit and the annuity term carries the balance to $17,175.24.
The Rule of 72
The Rule of 72 is the shortcut worth carrying in your head: divide 72 by the annual rate to estimate the years an amount takes to double. Here is how it scores against the true doubling time at five rates, with annual compounding.
- At 2%
- 36.0 est · 35.00 true
- At 5%
- 14.4 est · 14.21 true
- At 8%
- 9.0 est · 9.01 true
- At 10%
- 7.2 est · 7.27 true
- At 20%
- 3.6 est · 3.80 true
Closest at 8%; slightly long at low rates, slightly short at high ones. Fine for a mental check, wrong for anything you have to defend.
Questions people ask
What is compound interest?
Compound interest is interest calculated on both your original principal and the interest already added to the balance. Because each period earns interest on a larger amount than the last, the balance accelerates rather than growing in equal steps. The formula is balance = P × (1 + r ÷ n)^(n × years), where n is the number of compounding periods per year. At $1,000.00 and 5% over 10 years compounded monthly, that gives $1,647.01, including $647.01 of interest.
Covered in depth in How Does Compound Interest Work? The Math That Grows Money →
How is compound interest different from simple interest?
Simple interest is figured on the original principal alone, so it adds the same amount every period and climbs in a straight line. Compound interest adds each period of interest back to the balance, so the next period earns on a larger amount. Over a few months the two are nearly identical; over years the gap widens steadily. On $1,000.00 at 5% for 10 years, simple interest would pay $500.00 while monthly compounding pays $647.01. Use the simple interest calculator for growth that does not compound.
How much does $1,000 grow at 5% over 10 years?
Compounded monthly, $1,000.00 at 5% for 10 years grows to $1,647.01, which is $647.01 of interest. Compounded once a year instead it reaches $1,628.89, and compounded daily it reaches $1,648.66. If you also add $100.00 a month, the balance climbs to $17,175.24, of which $12,000.00 is your own deposits and $4,175.24 is interest. All four figures assume the rate holds steady for the whole decade, which no real account guarantees.
Does compounding frequency matter?
Less than people expect, and the effect flattens fast. On $1,000.00 at 5% over 10 years, annual compounding yields $1,628.89, quarterly $1,643.62, monthly $1,647.01, and daily $1,648.66. The whole span from annual to daily is $19.77, and going from daily to continuous compounding, the theoretical ceiling, adds six cents. The figure that folds frequency and rate together is the annual percentage yield, so comparing two accounts on APY rather than on the stated rate settles the question in one step.
What is the Rule of 72 and how accurate is it?
Divide 72 by the annual rate to estimate the years an amount takes to double. It is most accurate near 8%, where it gives 9.0 years against a true 9.01 with annual compounding. At 5% it gives 14.4 against 14.21, at 10% it gives 7.2 against 7.27, at 2% it gives 36.0 against 35.00, and at 20% it gives 3.6 against 3.80. So it runs slightly long at low rates and slightly short at high ones, which makes it a fine sanity check and a poor substitute for the formula.
Sources
Where the constants and formulas on this page come from. Each line names the figure it backs.
The definition of annual percentage yield as a rate reflecting total interest over a 365-day period given the rate and the compounding frequency.
Regulation DD, 12 CFR 1030.2 — Definitions — US Consumer Financial Protection Bureau
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