Compound Interest Calculator

$10,000 left for 10 years at 6% becomes $16,000 under simple interest and $17,908.48 under interest compounded once a year. Same money, same rate, same decade, $1,908.48 apart. Change nothing except how often the interest is added and the answer moves again: $18,193.97 compounded monthly, $18,220.29 compounded daily, $18,221.19 compounded continuously.

Those six numbers contain almost everything people mean when they ask about compounding. This guide works through all of them: the two formulas, every compounding frequency, the difference between a nominal rate, an effective rate and an APY, and the Rule of 72. Every figure below is arithmetic you can reproduce.

The Compound Interest Calculator on this page takes a starting amount, a monthly contribution, an annual rate and a number of years, and compounds monthly. That matches how most savings and investing actually works. For other frequencies, the formulas and tables here give you the answer directly.

Simple interest vs compound interest: what is the difference?

Simple interest is paid on your original amount only. It never pays on interest already earned, so it grows in a straight line, the same dollar amount every year forever.

Compound interest is paid on your balance plus the interest already added. The base keeps growing, so each year's interest is slightly larger than the last, and the growth curves upward instead of running flat.

For one year at the same rate, they are identical. The gap opens with time and it opens fast. Here is $10,000 at 6%, run both ways:

Years	Simple interest balance	Compounded annually	Gap
1	$10,600.00	$10,600.00	$0.00
5	$13,000.00	$13,382.26	$382.26
10	$16,000.00	$17,908.48	$1,908.48
20	$22,000.00	$32,071.35	$10,071.35
30	$28,000.00	$57,434.91	$29,434.91
40	$34,000.00	$102,857.18	$68,857.18

At 40 years the compounded balance is three times the simple one, from a rate that is identical. Nothing changed except that the interest was allowed to earn interest.

Simple interest is not a historical curiosity. It is still how many car loans, short-term personal loans, some bonds and most bridging finance are quoted. Compound interest is how savings accounts, credit cards, mortgages and every investment account work. Knowing which one you are looking at is the first question, before the rate.

Simple interest plus principal: the A = P(1 + rt) formula

When people search for a simple interest calculator, they usually want the total, principal and interest together, not the interest on its own. Two formulas, one after the other:

Interest: I = P x r x t Total, principal plus interest: A = P x (1 + r x t)

Where P is the principal, r is the annual rate as a decimal, and t is the time in years.

Worked through on $5,000 at 4% for 3 years:

• Interest: $5,000 x 0.04 x 3 = $600.00
• Total: $5,000 x (1 + 0.04 x 3) = $5,000 x 1.12 = $5,600.00

The same $5,000 at 4% for 3 years under compounding comes to $5,624.32 compounded annually, $5,636.36 compounded monthly, and $5,637.45 compounded daily. Over three years at a modest rate the compounding premium is $24 to $37. Over thirty years it is the difference in the table above. Short horizons hide the effect; long ones expose it.

For part-year terms, t is a fraction: 9 months is 0.75, 18 months is 1.5. Lenders quoting simple interest sometimes use a 360-day year, so a quoted daily figure can differ slightly from the same sum divided by 365. That is a convention difference, not an error, and it is worth asking about on any loan document rather than assuming.

The compound interest formula, written out

One formula covers every compounding frequency except continuous:

A = P x (1 + r/n)^(n x t)

• A is the final amount
• P is the principal, your starting balance
• r is the nominal annual rate as a decimal, so 6% is 0.06
• n is the number of compounding periods per year
• t is the number of years

The interest alone is A − P.

Worked through on $10,000 at 6% compounded quarterly for 10 years:

• Periodic rate: 0.06 ÷ 4 = 0.015, that is 1.5% per quarter
• Number of periods: 4 x 10 = 40
• Growth factor: 1.015^40 = 1.8140184
• Final amount: $10,000 x 1.8140184 = $18,140.18
• Interest earned: $8,140.18

When you are also adding money every month, a second term joins it. The future value of a stream of equal deposits made at the end of each period is:

Future value of contributions = C x ((1 + r)^n − 1) ÷ r

Where C is the deposit, r is the periodic rate and n is the number of periods. The calculator on this page adds the two together, growing your starting amount by the first formula and your monthly deposits by the second, then splits the result into what you put in and what the interest added.

Compound interest calculator with periodic compounding: how frequency changes the result

This is the table the question deserves. The same $10,000, the same 6% nominal rate, the same 10 years, compounded at every common frequency:

Compounding	Periods per year	Periodic rate	Balance after 10 years	Interest earned	Effective annual rate
Annually	1	6.0000%	$17,908.48	$7,908.48	6.0000%
Semi-annually	2	3.0000%	$18,061.11	$8,061.11	6.0900%
Quarterly	4	1.5000%	$18,140.18	$8,140.18	6.1364%
Monthly	12	0.5000%	$18,193.97	$8,193.97	6.1678%
Daily	365	0.016438%	$18,220.29	$8,220.29	6.1831%
Continuously	infinite	n/a	$18,221.19	$8,221.19	6.1837%

Two things are worth sitting with.

The first step is the big one. Going from annual to semi-annual compounding adds $152.63 over the decade. Going from monthly to daily adds $26.32. Going from daily all the way to continuous, an infinite number of compounding moments, adds 90 cents on $10,000 over ten years. The gains do not scale with frequency; they flatten almost immediately. Anyone advertising daily compounding as a meaningful advantage over monthly is selling you $26 per $10,000 per decade.

The total spread is small compared to the rate itself. Every frequency in that table sits between 6.00% and 6.19% effective. A quarter of a percentage point more on the headline rate beats any compounding frequency change. Shop the rate first, and treat frequency as a tiebreaker.

The calculator on this page compounds monthly, the fourth row. If your account compounds quarterly or daily, run the formula above for the exact figure, or accept that the monthly answer will be within a fraction of a percent either way.

Daily compound interest calculator: what daily compounding actually adds

Daily compounding means n = 365, so the periodic rate is your annual rate divided by 365 and the exponent is 365 times the number of years.

$10,000 at 5% compounded daily for one year:

• Daily rate: 0.05 ÷ 365 = 0.000136986
• Periods: 365
• Final amount: $10,000 x 1.000136986^365 = $10,512.67

Compare that with $10,500.00 at simple interest, and $10,511.62 compounded monthly. Daily compounding on a 5% account beats monthly by $1.05 per $10,000 per year. It is real, it is in your favour, and it is not a reason to move an account.

Over longer periods the same shape holds. $10,000 at 4% for 5 years comes to $12,166.53 compounded annually, $12,209.97 compounded monthly, and $12,213.89 compounded daily. The whole annual-to-daily spread across five years is $47.36, roughly what one extra tenth of a percentage point on the rate would have paid you.

Where daily compounding genuinely matters is on the other side of the ledger. Credit card balances are typically compounded daily, and there the base is growing at 20% or more rather than 5%, so the same mechanism works against you at four times the speed. If that is your situation, the Credit Card Payoff Calculator is the more useful tool.

Continuous compound interest calculator: the A = Pe^(rt) formula

Continuous compounding is the mathematical limit of the table above: what happens if you compound not daily, not hourly, but at every instant. The (1 + r/n)^n term converges on e, roughly 2.718282, and the formula collapses to something simpler than the periodic version:

A = P x e^(r x t)

Worked through on $10,000 at 6% for 10 years:

• Exponent: 0.06 x 10 = 0.6
• e^0.6 = 1.8221188
• Final amount: $10,000 x 1.8221188 = $18,221.19

Which, as the frequency table shows, is 90 cents more than daily compounding. Continuous compounding is not a product anyone sells you. No bank offers it. It is a modelling convenience, used in option pricing and academic finance because exponentials are far easier to work with than a compounding schedule, and because it gives a clean upper bound on what any frequency can produce.

Its practical use to a saver is exactly that upper bound. If continuous compounding at your rate does not get you to your goal, no compounding frequency will, and you need a different rate, a longer horizon, or more contributions. The Savings Goal Calculator works backwards from the target for you.

The matching continuous effective annual rate is e^r − 1, so 6% continuous is 6.1837% effective. To go the other way, from an effective rate to the continuous rate that produces it, take the natural log: a 6% effective annual return is ln(1.06) = 5.8269% continuous.

Nominal interest rate calculator: how to find the nominal rate

The nominal rate is the headline annual number, quoted before compounding is taken into account. It is a rate per year in name only, which is where the word comes from. 6% compounded monthly does not pay 6% in a year; it pays 6.1678%. The 6% is nominal.

If you know the effective annual rate and how often the account compounds, the nominal rate is:

Nominal rate = n x ((1 + EAR)^(1/n) − 1)

Worked through: what nominal rate, compounded monthly, produces a 6% effective annual return?

• 1.06^(1/12) = 1.00486755, so the monthly rate is 0.486755%
• Nominal annual rate: 0.486755% x 12 = 5.8411%

So 5.8411% compounded monthly and 6.0000% compounded annually are the same deal. The nominal number is lower and the money is identical, which is precisely why nominal rates should never be compared across different compounding schedules without converting first.

The other common use of "nominal" in finance is nominal versus real, meaning before and after inflation. Those are different concepts sharing a word. A 6% return with 3% inflation is roughly 3% real, more precisely 1.06 ÷ 1.03 − 1 = 2.913%. This guide uses nominal in the compounding sense throughout.

Effective interest rate calculator: turning a nominal rate into an effective annual rate

The effective annual rate, or EAR, is what you actually earn or pay in a year once compounding is included. It is the number that makes two differently compounded rates comparable, and it is the only rate worth putting side by side.

EAR = (1 + r/n)^n − 1

Where r is the nominal annual rate and n is compounding periods per year.

Worked through on a credit card quoted at 18% APR, compounded monthly:

• Monthly periodic rate: 0.18 ÷ 12 = 1.5%
• EAR: 1.015^12 − 1 = 1.1956182 − 1 = 19.5618%

So an 18% card costs 19.56% a year if you carry the balance and never pay it down. That 1.56 percentage point gap is the compounding, and it is the number card statements do not lead with.

The same conversion applied to the frequencies in the table above turns one 6% nominal rate into six different effective rates, from 6.0000% to 6.1837%. Whenever you are comparing two accounts or two loans, convert both to EAR first. Comparing a monthly-compounded rate against a quarterly-compounded one at face value is comparing two different things.

APY vs interest rate: why are they different numbers?

They measure different things, and US banks are required to publish both, which is why you see them together and why they never match.

• The interest rate is the nominal rate. It is the rate applied to your balance at each compounding step, annualised by simple multiplication.
• The APY, annual percentage yield, is the effective annual rate. It already includes the effect of compounding. It is what a $100 deposit actually becomes after one untouched year.

APY is always the higher of the two, unless the account compounds exactly once a year, in which case they are equal. The formula is the EAR formula wearing a different name:

APY = (1 + r/n)^n − 1

Nominal rate	Compounding	APY
5.00%	Annually	5.0000%
5.00%	Monthly	5.1162%
5.00%	Daily	5.1267%
4.8889%	Monthly	5.0000%

Read the last row carefully, because it is the whole point. A bank advertising 5.00% APY with monthly compounding is paying a nominal rate of 4.8889%. Both numbers describe the same account. The bank leads with APY because it is the larger, more attractive figure, and because it is the honest one for comparison, both things are true at once.

On the borrowing side the incentive flips. Lenders quote APR, which for most consumer credit is a nominal rate plus certain fees, and which does not include the effect of compounding the way APY does. The higher number is quiet on the loan and loud on the deposit.

Practical rule: compare deposits by APY and only by APY. If a bank gives you only a nominal rate, convert it. If two accounts show the same APY, the compounding frequency is already baked in and does not break the tie.

Periodic interest rate calculator: nominal rate divided by periods per year

The periodic rate is the rate actually applied at each compounding step, and it is the input every compound interest formula really wants:

Periodic rate = nominal annual rate ÷ periods per year

Nominal annual rate	Compounding	Periods per year	Periodic rate
6%	Semi-annually	2	3.0000%
6%	Quarterly	4	1.5000%
6%	Monthly	12	0.5000%
6%	Daily	365	0.016438%
18%	Monthly	12	1.5000%
24%	Daily	365	0.065753%

Two conventions to watch. First, some lenders divide by 360 rather than 365 for daily rates, which makes each day's charge fractionally larger. Second, a monthly periodic rate on a card statement is sometimes shown to only two decimals, so recomputing a statement from the rounded figure can leave you a few cents adrift. Neither is a reason for alarm; both are reasons to work from the nominal rate rather than the rounded periodic one.

Note what the periodic rate is not. Multiplying it back by the number of periods returns the nominal rate, never the effective one. 1.5% a month is 18% nominal and 19.5618% effective, and only the last of those tells you what a year of carried balance costs.

Equivalent interest rate calculator: matching rates across different compounding

Two rates are equivalent when they produce the same balance over the same time despite compounding at different frequencies. This is the conversion you need whenever a comparison involves two different schedules.

Go from any frequency to any other in two steps. First convert to an effective annual rate, then convert back out:

Step 1: EAR = (1 + r₁/n₁)^n₁ − 1 Step 2: r₂ = n₂ x ((1 + EAR)^(1/n₂) − 1)

Worked through: a bond quoted at 6% compounded semi-annually, restated as a monthly-compounded rate.

• EAR: 1.03^2 − 1 = 6.0900%
• Monthly periodic rate: 1.0609^(1/12) − 1 = 0.493862%
• Nominal rate compounded monthly: 0.493862% x 12 = 5.9263%

So 6% semi-annual and 5.9263% monthly are the same investment. Here are the common equivalents of a 6.0900% effective annual rate, which is what 6% semi-annual produces:

Stated as	Equivalent nominal rate
Compounded annually	6.0900%
Compounded semi-annually	6.0000%
Compounded quarterly	5.9557%
Compounded monthly	5.9263%
Compounded daily	5.9122%
Continuously	5.9118%

Every row in that table is the same return. The stated rate falls as the frequency rises because more frequent compounding needs a smaller nominal rate to reach the same place.

Savings interest rate calculator: what rate did my savings actually earn?

Sometimes you have the start, the end and the elapsed time, and what you want is the rate. Rearranging the compound interest formula, with no deposits or withdrawals in between:

Annual rate = (Ending balance ÷ Starting balance)^(1/t) − 1

Worked through on $10,000 that became $12,000 over 3 years:

• Ratio: $12,000 ÷ $10,000 = 1.2
• 1.2^(1/3) = 1.0626586
• Annual rate: 6.2659%

Note that this is not 20% ÷ 3 = 6.67%. Dividing total growth by years overstates the rate every time, because it ignores that the later years were growing from a larger base. The gap widens with the horizon.

Two caveats. This only works if nothing went in or out during the period. If you were also making deposits, the rate you want is a money-weighted return and the Investment ROI Calculator is the right tool. And this gives you the effective annual rate, which is what you want for comparison, not the nominal rate your bank prints.

To go the other way, from a rate to a dollar figure: $10,000 in an account paying 4.50% APY, untouched for a year, earns $450.00 and ends at $10,450.00. Because APY already includes compounding, no further adjustment is needed, multiply and you are done.

How much does $10,000 plus $500 a month grow to in 20 years?

The tables above hold contributions at zero to isolate the compounding. Real saving rarely looks like that. Here is the calculator's default scenario: start with $10,000, add $500 a month, assume a 7% annual return, run it for 20 years.

• Total you put in: $10,000 + ($500 x 240 months) = $130,000
• Ending balance: $300,850.60
• Interest: $170,850.60

More of the final balance is interest than is your own money, and that crossover is the thing worth understanding. It happens because the earliest dollars have the longest time to multiply. The $500 you deposit in month one compounds for 240 months; the one you deposit in month 239 compounds for one. Starting earlier is worth more than contributing more, over any horizon long enough for the curve to bend.

That is the one variable you can never get back. Rate is uncertain, contribution is constrained by income, but start date is a decision available today and only today.

What is the Rule of 72, and when does it stop working?

The Rule of 72 is the mental shortcut: divide 72 by the annual percentage rate to get the approximate number of years for money to double. At 6%, 72 ÷ 6 = 12 years. At 9%, 8 years. No calculator, no exponent.

It is an approximation of ln(2) ÷ ln(1 + r), and here is exactly how close:

Annual rate	Rule of 72 estimate	Actual years to double	Off by
1%	72.0	69.66	2.3 years too slow
2%	36.0	35.00	1.0 years too slow
4%	18.0	17.67	0.3 years too slow
6%	12.0	11.90	0.1 years too slow
8%	9.0	9.01	essentially exact
10%	7.2	7.27	0.1 years too fast
12%	6.0	6.12	0.1 years too fast
15%	4.8	4.96	0.2 years too fast
20%	3.6	3.80	0.2 years too fast

The rule is calibrated to be exact at about 8%, and drifts in both directions from there. Between roughly 4% and 15% it is within a quarter of a year, which is far better than the precision of any return assumption you would feed it. Below 3% it is genuinely poor, off by more than two years at 1%, and the Rule of 70 is the better shortcut down there. Above 20% it runs optimistic and should not be trusted at all.

Under continuous compounding the exact constant is 69.3, because ln(2) = 0.693. At 6% continuous, doubling takes 69.3 ÷ 6 = 11.55 years. 72 survives as the popular version because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which matters when the whole point is doing it in your head.

One thing the rule cannot do is handle contributions. It answers "how long for this pile to double", not "how long until my monthly saving gets me to a target". For that, use the calculator on this page or the Savings Goal Calculator.

What rate should you use?

For a savings account or CD, use the APY the bank publishes, not the nominal rate. It is the honest figure and it is already compounding-adjusted.

For long-term stock market investing, a commonly used planning assumption is around 7% after inflation, which is lower than headline historical averages precisely because it strips inflation out. Whatever number you pick, be clear with yourself about whether it is nominal or real, and keep your contributions and your target on the same basis. Mixing a nominal return with a real-terms goal quietly overstates the outcome.

The real caution is not the level of the rate but its steadiness. These formulas assume a constant rate, and no investment delivers one. The average can hold over 20 years while individual years swing violently either side of it, and the order in which those years arrive matters a great deal if you are drawing money out. Treat the output as a central estimate, not a forecast, and run a pessimistic rate alongside your main one.

Common mistakes

Comparing two nominal rates with different compounding. 5.90% compounded monthly beats 5.95% compounded annually. Convert both to effective annual rates before deciding anything.

Dividing total growth by the number of years. $10,000 to $12,000 over 3 years is 6.27% a year, not 6.67%. The shortcut ignores the growing base and overstates the rate on every multi-year period.

Treating APR on a loan as if it were APY. APR is generally a nominal rate plus certain fees and does not include compounding the way APY does. On an 18% card, the compounding takes the real annual cost to 19.56%.

Chasing daily compounding. On $10,000 at 5%, daily compounding beats monthly by about $1 a year. A 0.10 percentage point better rate beats it ten times over. Shop the rate, not the frequency.

Using simple interest math on a compounding product. Estimating a 30-year savings balance with P x r x t understates it by more than half at 6%, $28,000 against $57,434.91.

Forgetting that the same math runs on debt. Every table here works identically against you on a credit card or a revolving balance, at a much higher rate and usually compounded daily.

Assuming the average return arrives evenly. A 7% average is not 7% every year, and if you are withdrawing money, a bad run early does lasting damage that the average alone will never show you.

Related calculators

• Savings Goal Calculator: work backwards from a target to the monthly deposit it needs
• Investment ROI Calculator: annualised return on an investment you already made
• Retirement Calculator: the same compounding math applied over a working lifetime
• Credit Card Payoff Calculator: compounding running the other direction, and what it costs to stop it
• Loan Payoff Calculator: what extra payments do to total interest on a term loan
• Percentage Calculator: quick percentage-of and percentage-change arithmetic