How compound interest is calculated
For a single starting amount with nothing added, one formula gives the answer.
- P is the principal, the amount you start with.
- r is the yearly interest rate written as a decimal. 4% is 0.04.
- n is the number of times interest is added each year: 1 for yearly, 12 for monthly, 365 for daily.
- t is the time in years.
- A is the amount you end with. Subtract P to get the interest.
The part in brackets is the growth in one compounding period. The power, n times t, is the number of periods. More periods means the interest joins the balance sooner and starts earning sooner.
Monthly deposits do not fit one tidy formula, so the calculator goes month by month:
- Turn the yearly rate into the growth for one month at your compounding frequency.Monthly growth = (1 + r/n)^(n/12)
- Multiply the balance by that figure.
- Add the monthly deposit at the end of the month.
- Repeat for every month, and record the balance at the end of each year.
The calculator runs these steps three times, with n set to 365, 12 and 1, so you can compare the results without retyping anything.
Worked examples
The interest rates below are examples chosen to show the maths. They are not rates on offer.
$10,000 left alone for 10 years at 5%
No monthly deposits. The last row uses yearly compounding, which is 10,000 × 1.05^10.
- Money paid in$10,000
- Balance with yearly compounding$16,289
- Balance with monthly compounding$16,470
- Balance with daily compounding$16,487
- Daily ahead of yearly by$198
- Interest earned (yearly compounding)$6,289
$200 a month for 20 years at 4%
Starting from nothing, with monthly compounding. Deposits are a much larger share of the result here.
- Money paid in$48,000
- Balance with yearly compounding$72,768
- Balance with monthly compounding$73,355
- Balance with daily compounding$73,408
- Daily ahead of yearly by$640
- Interest earned (monthly compounding)$25,355
$5,000 plus $150 a month for 5 years at 3.5%
A shorter stretch with daily compounding. Over five years the three frequencies finish close together.
- Money paid in$14,000
- Balance with yearly compounding$15,745
- Balance with monthly compounding$15,775
- Balance with daily compounding$15,777
- Daily ahead of yearly by$33
- Interest earned (daily compounding)$1,777
Daily, monthly and yearly compounding by rate
This table shows $10,000 left for 10 years with no deposits. Read across a row to see what the frequency does. Read down a column to see what the rate does.
| Interest rate | Yearly compounding | Monthly compounding | Daily compounding | Daily ahead of yearly by |
|---|---|---|---|---|
| 1% | $11,046 | $11,051 | $11,052 | $5 |
| 2% | $12,190 | $12,212 | $12,214 | $24 |
| 3% | $13,439 | $13,494 | $13,498 | $59 |
| 4% | $14,802 | $14,908 | $14,918 | $115 |
| 5% | $16,289 | $16,470 | $16,487 | $198 |
| 6% | $17,908 | $18,194 | $18,220 | $312 |
| 7% | $19,672 | $20,097 | $20,136 | $465 |
| 8% | $21,589 | $22,196 | $22,253 | $664 |
Moving from yearly to daily at 4% adds $115 over ten years. Moving from 4% to 5% adds more than ten times that. The gap between frequencies does grow as the rate and the time go up, because there is more interest to compound.
Daily compounding and how banks apply it
With daily compounding the bank works out one day of interest, adds it to the balance used for the next day, and repeats. The daily rate is the yearly interest rate divided by 365.
On $10,000 at 4% the first day earns about $1.10. The second day earns interest on $10,000 plus that first day of interest, which comes to $1.0960 against $1.0959. The gain from one day to the next is tiny. Repeated 365 times it turns $400 of simple interest into about $408.08.
Four points from the federal rules for US bank accounts (Regulation DD) are worth knowing:
- The daily rate has a floor. Banks must use a daily rate of at least 1/365 of the interest rate. In a leap year they may use 1/366.
- Interest is figured on the full balance each day. Banks use either the daily balance method, which applies the daily rate to each day's balance, or the average daily balance method, which applies it to the average balance over the period.
- No frequency is required. The rules do not make banks compound or credit interest on any particular schedule. They do make banks tell you the schedule.
- Compounding and crediting are different things. An account can compound daily and credit monthly. The interest is worked out each day, but it shows up in your balance once a month.
If closing the account before interest is credited means you lose that interest, the bank has to say so in its account disclosures. Check them before you move your money.
Simple interest and compound interest
Simple interest pays the rate on your original money only. Take $10,000 at 5% for 10 years. Simple interest is 10,000 × 0.05 × 10, which is $5,000. With yearly compounding the interest is $6,289. The extra $1,289 is interest earned on earlier interest.
That extra part starts small and speeds up. Over 30 years on the same numbers, simple interest pays $15,000 and compound interest pays $33,219. The calculator shows both lines so you can see how much of your result comes from compounding.
The Rule of 72
The Rule of 72 estimates how long money takes to double. Divide 72 by the yearly rate. At 6% the answer is 12 years. The US Securities and Exchange Commission describes it as a way to tell approximately how long doubling takes.
| Interest rate | Rule of 72 | Exact, yearly compounding | Exact, daily compounding |
|---|---|---|---|
| 2% | 36.0 years | 35.0 years | 34.7 years |
| 3% | 24.0 years | 23.4 years | 23.1 years |
| 4% | 18.0 years | 17.7 years | 17.3 years |
| 6% | 12.0 years | 11.9 years | 11.6 years |
| 8% | 9.0 years | 9.0 years | 8.7 years |
| 10% | 7.2 years | 7.3 years | 6.9 years |
| 12% | 6.0 years | 6.1 years | 5.8 years |
The rule is closest for yearly compounding at rates around 8%. At low rates it gives a figure that is a little too long, and at high rates one that is too short. Use it for a quick check in your head, and use the formula when the answer matters.
What the result leaves out
- Rate changes. The sum uses one rate for the whole period. Most savings rates are variable and move over time.
- Tax. Interest on savings is taxable income in the US. Tax paid from the account slows the growth.
- Inflation. The result is in future dollars, which will buy less than the same number of dollars today.
- Fees and withdrawals. Neither is deducted.
- Deposit timing. Deposits are counted at the end of each month. Paying in at the start of the month earns a little more.
- Day counts. Daily compounding uses 365 equal days and every month counts as one twelfth of a year. A bank works from the actual days, so its figure can differ from this one by cents.
Common mistakes
- Entering the APY as the interest rate. The APY already includes compounding. Enter it here with daily compounding and the interest is counted twice. If you only know the APY, choose yearly compounding.
- Expecting daily compounding to change the result a lot. At 4% the gain over monthly compounding averages about $0.96 a year on $10,000 over ten years.
- Using a percentage where the formula needs a decimal. In the formula, 4% is 0.04, not 4.
- Treating the Rule of 72 as exact. It is an estimate, and it ignores deposits.
- Mixing up compounding and crediting. Monthly crediting does not mean monthly compounding.
Questions people ask
What is the compound interest formula?
A = P(1 + r/n)^(nt). P is the starting amount, r is the yearly interest rate as a decimal, n is how many times a year interest is added, and t is the number of years. A is the balance at the end.
How do I calculate daily compound interest?
Divide the yearly rate by 365 to get the daily rate, add 1, raise it to the number of days, and multiply by your balance. At 4%, $10,000 earns about $1.10 on the first day and about $408.08 over a full year.
Is daily compounding better than monthly?
Yes, but only slightly. On $10,000 at 4% for 10 years, daily compounding ends about $10 ahead of monthly. A small difference in the interest rate matters much more than the compounding frequency.
What is the difference between simple and compound interest?
Simple interest is paid only on the money you put in. Compound interest is also paid on the interest already added to the balance, so the amount earning interest keeps growing.
What is the Rule of 72?
It is a quick estimate of how long money takes to double. Divide 72 by the yearly rate. At 6% that gives 12 years. It is an approximation, and the exact answer at 6% with yearly compounding is about 11.9 years.
How much will $10,000 be worth in 10 years at 5%?
With yearly compounding, $16,289. With daily compounding, $16,487. That assumes nothing is added or taken out and the rate stays at 5% for the whole 10 years. 5% is an example, not a rate on offer.
Do banks compound savings interest daily?
Many do, but there is no federal rule that says how often a bank must compound. Federal rules require the bank to tell you how often interest is compounded and how often it is credited to your account.
Does compound interest work against me on debt?
Yes. The same maths applies to money you owe. When unpaid interest is added to a debt, you pay interest on that interest as well. This page covers savings only.
Related calculators
Sources
- Investor.gov (U.S. Securities and Exchange Commission): compound interest calculator
- Investor.gov: What is compound interest? (includes the Rule of 72)
- Investor.gov glossary: compound interest
- Consumer Financial Protection Bureau: Regulation DD, section 1030.7, payment of interest
- Consumer Financial Protection Bureau: Regulation DD, section 1030.4, account disclosures
- Consumer Financial Protection Bureau: Regulation DD, section 1030.2, definitions
- IRS Topic no. 403: Interest received
Figures last checked against these sources on October 10, 2026. This page gives general information and estimates, not tax, legal or financial advice.