On this page
Formula
A = P(1 + r/n)^(n × t) for a lump sum; with contributions, each month B = B × (1 + i) + C, where i = (1 + APY)^(1/12) − 1 and APY = (1 + r/n)^n − 1
- A
- the balance at the end of the period, with no contributions
- P
- the initial deposit
- r
- the nominal annual interest rate as a decimal (5% = 0.05)
- n
- compounding periods per year (1, 2, 4, 12 or 365); for continuous compounding APY = e^r − 1
- t
- the number of years
- B
- the running balance, updated once a month
- C
- the monthly contribution, added at the end of each month
- i
- the monthly growth rate equivalent to the chosen compounding
How compound interest works
With compound interest, the interest you earn is added to the balance, and the next round of interest is calculated on that larger balance. Each period you earn interest on your original deposit and on all the interest added before it.
At 5% a year compounded annually, $1,000 earns $50 in the first year. In the second year it earns 5% of $1,050, which is $52.50. The extra $2.50 is interest on interest. The effect is small at first but grows every year, which is why the balance curve bends upward over long periods. For a side-by-side comparison with interest that does not compound, see simple vs. compound interest.
What the inputs mean
- Initial deposit. The amount you start with. It can be $0 if you are only making monthly contributions.
- Annual interest rate. The nominal yearly rate, as quoted before compounding. If an account quotes only an APY, choose Annually as the compounding frequency and enter the APY as the rate.
- Years. How long the money stays invested, in whole years.
- Compounding. How often interest is added to the balance: annually, semiannually, quarterly, monthly, daily or continuously.
- Monthly contribution. An optional fixed amount added at the end of every month.
Reading the results
The headline figure is the balance at the end of the period. Below it, Total deposits is everything you put in (the initial deposit plus all contributions), and Interest earned is the difference between the final balance and your deposits.
Effective annual rate (APY) shows how much a single deposit grows in one year once compounding is included. It is the figure banks use so savers can compare accounts. The year-by-year table shows when interest starts to make up a large share of the balance.
Compound interest with monthly contributions
When you add a monthly contribution, the compound interest calculator works month by month. Each month it applies one month of growth to the balance, then adds that month’s contribution. Because the deposit arrives at the end of the month, it first earns interest in the following month. End-of-month deposits match how many people save, such as a transfer after payday, and are the conservative choice: if you deposit at the start of each month instead, your actual balance will be slightly higher.
To keep the stated compounding frequency accurate on a monthly timeline, the calculator converts your rate into the monthly rate that gives the same APY. With no contributions, the result is identical to the standard formula P(1 + r/n)^(n × t). Contributions grow at that same equivalent monthly rate. A real account that compounds quarterly or annually may credit interest on mid-period deposits differently, so its balance can differ slightly.
Reference tables
All figures below were produced with the same method the calculator uses and are rounded to the cent. They assume a constant rate, no withdrawals, no fees and no taxes.
Growth of a $10,000 lump sum
Interest compounded monthly, no further deposits.
| Annual rate | 5 years | 10 years | 20 years | 30 years |
|---|---|---|---|---|
| 3% | $11,616.17 | $13,493.54 | $18,207.55 | $24,568.42 |
| 5% | $12,833.59 | $16,470.09 | $27,126.40 | $44,677.44 |
| 7% | $14,176.25 | $20,096.61 | $40,387.39 | $81,164.97 |
Over 30 years, the 7% column ends at more than three times the 3% column, even though the rate is a little over twice as high. That widening gap is the compounding effect at work.
Saving $200 a month from zero
$200 added at the end of every month, interest compounded monthly.
| Annual rate | 5 years | 10 years | 20 years | 30 years |
|---|---|---|---|---|
| Total deposited | $12,000 | $24,000 | $48,000 | $72,000 |
| 3% | $12,929.34 | $27,948.28 | $65,660.40 | $116,547.38 |
| 5% | $13,601.22 | $31,056.46 | $82,206.73 | $166,451.73 |
| 7% | $14,318.58 | $34,616.96 | $104,185.33 | $243,994.20 |
At 7%, the extra 10 years between the 20-year and 30-year columns add $24,000 of deposits but about $139,800 to the balance.
Daily, monthly and quarterly compounding compared
| Compounding | APY at a 5% rate | APY at a 6% rate | $10,000 at 5% after 10 years |
|---|---|---|---|
| Annually | 5% | 6% | $16,288.95 |
| Semiannually | 5.0625% | 6.09% | $16,386.16 |
| Quarterly | 5.0945% | 6.1364% | $16,436.19 |
| Monthly | 5.1162% | 6.1678% | $16,470.09 |
| Daily (365) | 5.1267% | 6.1831% | $16,486.65 |
| Continuously | 5.1271% | 6.1837% | $16,487.21 |
Moving from annual to monthly compounding adds about $181 over 10 years on $10,000 at 5%. Moving from monthly to continuous adds about $17 more.
How to calculate compound interest by hand
Take $2,500 at 4.8% a year, compounded quarterly, for 3 years.
- Find the rate per period: 0.048 ÷ 4 = 0.012.
- Count the periods: 4 × 3 = 12 quarters.
- Raise the growth factor to that power: 1.012^12 ≈ 1.153895.
- Multiply by the deposit: $2,500 × 1.153895 ≈ $2,884.74.
- Interest earned is $2,884.74 − $2,500 = $384.74.
The APY for this account is (1.012)^4 − 1 ≈ 4.8871%. Entering the same inputs in the compound interest calculator returns $2,884.74.
Real-life scenarios
A CD compared with a savings account
Suppose $10,000 could go into a 2-year certificate of deposit at 4.25% compounded monthly, or a savings account at 3.5% compounded daily. If both rates held for the full two years, the CD would end at $10,885.54 and the savings account at $10,725.05, a difference of about $160. The comparison has limits: a savings account rate is usually variable and can rise or fall, while a CD typically fixes the rate but charges a penalty if you withdraw before maturity. The calculator shows only the growth under a constant rate. Federal deposit insurance at banks generally covers up to $250,000 per depositor, per insured bank, for each account ownership category.
Starting earlier with the same monthly amount
Two savers each put $200 a month into an account earning a steady 7%. The one who saves for 30 years deposits $72,000 and ends with $243,994.20. The one who saves for 20 years deposits $48,000 and ends with $104,185.33. The extra 10 years add only $24,000 of deposits but account for more than half of the larger balance, because the earliest deposits compound the longest.
A balance that already exists
$15,000 already saved, plus $250 a month for 20 years at 6% compounded monthly, grows to $165,163.29 in the calculator: $75,000 of deposits and $90,163.29 of interest. This case appears in the worked examples below.
The rule of 72
Dividing 72 by the annual rate in percent gives a rough number of years for a lump sum to double. At 6% the estimate is 12 years against an exact 11.9 years with annual compounding; at 9% it is 8 years against 8.04. The rule is a mental shortcut, not a substitute for the calculation, and it drifts further from the exact answer at very low or very high rates.
What moves the result most
- Time. Interest on interest builds slowly, so the later years of a long period add far more than the early ones.
- Rate. A difference of one or two percentage points becomes a large gap over decades.
- Regular contributions. Over shorter periods, steady deposits usually add more to the balance than interest does.
- Compounding frequency. This has the smallest effect of the four.
To see the total growth as a single percentage, enter your starting and ending figures in the percentage change calculator. To measure a result you have already achieved, the ROI calculator turns a start and end value into an annualized rate.
Common mistakes
- Applying compounding to an APY. An APY already includes compounding. Enter it with annual compounding.
- Treating the projection as a forecast. Savings rates change and investment returns vary from year to year. The result shows what a constant rate would produce, not what will happen.
- Ignoring taxes and inflation. A nominal balance overstates future purchasing power, especially over long periods.
- Comparing accounts by rate instead of APY. Two accounts with the same rate but different compounding have different APYs; the APY is the comparable figure. The guide to APR vs. APY covers this in more detail.
Glossary
- Principal. The original amount deposited, before any interest.
- Nominal rate. The stated annual rate before the effect of compounding.
- Compounding period. How often earned interest is added to the balance.
- APY (annual percentage yield). The one-year growth rate including compounding. Banks disclose it so accounts can be compared on the same basis.
- Effective annual rate. The general term for the same idea as APY, used for both savings and borrowing.
Worked examples
A lump sum left to grow
$10,000 at 5% a year, compounded monthly, for 10 years, with no extra deposits.
Inputs: Initial deposit = $10000; Annual interest rate = 5 %; Years = 10 years; Compounding = Monthly (12×/year); Monthly contribution = $0
Answer: $10,000.00 at 5% compounded monthly grows to $16,470.09 after 10 years ($6,470.09 interest).
Saving a fixed amount each month
$200 deposited at the end of every month for 5 years at 4%, compounded monthly.
Inputs: Initial deposit = $0; Annual interest rate = 4 %; Years = 5 years; Compounding = Monthly (12×/year); Monthly contribution = $200
Answer: $0.00 at 4% compounded monthly with $200.00/month grows to $13,259.80 after 5 years ($1,259.80 interest).
A three-year certificate of deposit
$5,000 placed in a 3-year CD paying 4.5% compounded daily, with interest left in the account until maturity.
Inputs: Initial deposit = $5000; Annual interest rate = 4.5 %; Years = 3 years; Compounding = Daily (365×/year); Monthly contribution = $0
Answer: $5,000.00 at 4.5% compounded daily grows to $5,722.64 after 3 years ($722.64 interest).
A starting balance plus regular monthly saving
$15,000 already saved, plus $250 at the end of every month for 20 years, at a steady 6% compounded monthly.
Inputs: Initial deposit = $15000; Annual interest rate = 6 %; Years = 20 years; Compounding = Monthly (12×/year); Monthly contribution = $250
Answer: $15,000.00 at 6% compounded monthly with $250.00/month grows to $165,163.29 after 20 years ($90,163.29 interest).
Assumptions and limitations
- The interest rate stays the same for the whole period. Real savings rates and investment returns change over time.
- Monthly contributions are added at the end of each month, so a deposit starts earning interest the following month. Contributions are the same amount every month.
- Interest is applied using the monthly rate that produces the same annual growth as the compounding you select. With no contributions, the final balance equals P(1 + r/n)^(n × t) exactly.
- Daily compounding uses 365 periods a year. Continuous compounding uses an effective annual rate of e^r − 1.
- The period is a whole number of years, from 1 to 100.
- Taxes on interest, account fees, inflation and withdrawals are not modeled. The result is a nominal (not inflation-adjusted) balance.
Frequently asked questions
What is the difference between the interest rate and APY?
The interest rate is the nominal annual rate before compounding. APY (annual percentage yield) is the growth you actually get over one year once compounding is included. A 6% rate compounded monthly gives an APY of about 6.17%. Comparing APYs lets you compare accounts that compound at different frequencies.
How much difference does compounding frequency make?
Less than many people expect. At 6%, moving from annual to monthly compounding raises the APY from 6.00% to about 6.17%, and daily or continuous compounding adds only about another 0.02 percentage points. The rate itself and the length of time matter far more.
How do you calculate compound interest on a CD?
Enter the deposit, the CD's rate, its compounding frequency and the term in years. $10,000 in a 2-year CD at 4.25% compounded monthly grows to $10,885.54, which is $885.54 of interest. If the bank quotes only an APY, enter it with annual compounding. Terms shorter than a year can't be entered, because the period must be a whole number of years.
Can I use this to project stock market returns?
Only as a rough illustration. The calculator assumes the same return every year. Investments that can rise and fall do not grow at a steady rate, and the order of good and bad years affects the outcome when you are adding money over time.
My bank quotes only an APY. What should I enter?
Enter the APY as the annual rate and set compounding to Annually. An APY already includes the effect of compounding, so applying another compounding step on top of it would overstate the growth slightly.
How do you calculate compound interest on a loan?
Most installment loans, such as car loans and mortgages, charge each month's interest on the balance still owed and are paid down every month, so interest does not pile up on itself the way it does in savings. The [loan calculator](/loan-calculator/) works out the payment and total interest for those. Interest compounds on a debt only when unpaid interest is added to the balance, as with a credit card balance carried from month to month.
Does the result account for inflation or taxes?
No. The balance is nominal and pre-tax. Interest on most savings accounts and CDs is taxable in the year it is credited, and inflation reduces what a future balance can buy, so the real value of the result is lower than the figure shown.
Sources
- Compound Interest (glossary) — U.S. Securities and Exchange Commission, Investor.gov. Checked October 4, 2026.
- Appendix A to Part 1030 — Annual Percentage Yield Calculation — Consumer Financial Protection Bureau. Checked October 4, 2026.
- Understanding Deposit Insurance — Federal Deposit Insurance Corporation. Checked October 4, 2026.
- Certificates of Deposit (CDs) — U.S. Securities and Exchange Commission, Investor.gov. Checked October 4, 2026.