Calculate compound interest: the future value of a deposit plus regular contributions at any compounding frequency, including daily and continuous.
After 10 years the balance is $54,713.58: $34,000.00 you put in and $20,713.58 of interest, which is 37.9% of the final balance.
| Year | Deposits | Interest | Total deposits | Balance |
|---|---|---|---|---|
| 1 | $2,400.00 | $801.42 | $12,400.00 | $13,201.42 |
| 2 | $2,400.00 | $1,032.85 | $14,800.00 | $16,634.27 |
| 3 | $2,400.00 | $1,281.01 | $17,200.00 | $20,315.28 |
| 4 | $2,400.00 | $1,547.11 | $19,600.00 | $24,262.39 |
| 5 | $2,400.00 | $1,832.45 | $22,000.00 | $28,494.83 |
| 6 | $2,400.00 | $2,138.41 | $24,400.00 | $33,033.24 |
| 7 | $2,400.00 | $2,466.49 | $26,800.00 | $37,899.74 |
| 8 | $2,400.00 | $2,818.29 | $29,200.00 | $43,118.03 |
| 9 | $2,400.00 | $3,195.52 | $31,600.00 | $48,713.55 |
| 10 | $2,400.00 | $3,600.02 | $34,000.00 | $54,713.58 |
Converts the nominal rate to the equivalent rate over one contribution interval, so any compounding frequency works with any contribution frequency.
Money shown rounded half-to-even to 2 decimals; nothing is rounded before this line.
Compound interest adds each period's interest to the balance, so later interest is earned on earlier interest. A single deposit grows to A = P(1 + r/k)^(kt) at annual rate r compounded k times a year for t years, or P × e^(rt) with continuous compounding. Regular contributions are added as an annuity at the equivalent rate per contribution period, paid at the start or the end of each period.
With the defaults, 10,000 at 7% compounded monthly plus 200 at the end of each month grows to 54,713.58 in 10 years. Deposits total 34,000.00, so 20,713.58, or 37.9% of the final balance, is interest. The effective annual rate is 7.2290%.
The rate is held constant and no tax or fees are deducted. Investment returns vary from year to year, so for anything other than a fixed-rate account the result shows what a steady average rate would produce.
Take 5,000 at 6% a year compounded quarterly for 8 years, plus 100 paid in at the end of every month. The deposit and the contributions are handled separately and then added.
Skipping step 3 and using 6% ÷ 12 = 0.5% a month for the contributions gives 12,282.85, which is 15.54 too much, because it switches the contributions to monthly compounding. The calculator converts the rate for every pairing of compounding and contribution frequency, so the two parts always use the same underlying rate.
Rearranging A = P(1 + r/k)^(kt) answers the two other common questions:
Spreadsheets have the conversions built in. =EFFECT(6%, 4) returns the 6.1364% effective rate of the worked example, and =NOMINAL(EFFECT(6%, 4), 12) returns 5.9702%, which is 12 times the monthly contribution rate from step 3. The time value of money calculator solves for the rate or the time of a lump sum directly.
The effective annual rate is what the nominal rate actually earns in a year once compounding is included: (1 + r/k)^k − 1 for k periods a year, or e^r − 1 for continuous compounding. Each cell below is that percentage:
| Nominal rate | Yearly | Half-yearly | Quarterly | Monthly | Daily (365) | Continuous |
|---|---|---|---|---|---|---|
| 2% | 2.0000 | 2.0100 | 2.0151 | 2.0184 | 2.0201 | 2.0201 |
| 4% | 4.0000 | 4.0400 | 4.0604 | 4.0742 | 4.0808 | 4.0811 |
| 6% | 6.0000 | 6.0900 | 6.1364 | 6.1678 | 6.1831 | 6.1837 |
| 8% | 8.0000 | 8.1600 | 8.2432 | 8.3000 | 8.3278 | 8.3287 |
| 10% | 10.0000 | 10.2500 | 10.3813 | 10.4713 | 10.5156 | 10.5171 |
| 12% | 12.0000 | 12.3600 | 12.5509 | 12.6825 | 12.7475 | 12.7497 |
Frequency matters more as the rate rises. At 2% the whole spread from yearly to continuous is 0.02 points; at 12% it is 0.75 points. Past daily compounding there is almost nothing left to gain.
US banks must quote savings yields as an annual percentage yield. Regulation DD defines it as APY = 100 × ((1 + interest ÷ principal)^(365 ÷ days in term) − 1) (12 CFR 1030, Appendix A). The regulation's own example: 30.37 of interest on 1,000 over a 182-day certificate is an APY of 6.18%. For an account with no fees and a constant rate, the APY equals this calculator's effective annual rate. A 5% rate compounded daily shows 5.1267%, and 1,000 left for a year earns 51.27.
Two offers are only comparable on the effective rate. A 4.95% account compounded monthly (5.0639% effective) beats a 5% account compounded yearly (5.0000%), even though its headline rate is lower. Where a lender quotes only a nominal rate, enter it with the stated compounding and read the effective annual rate off the result.
Dividing 72 by the annual rate estimates how many years money takes to double. The exact time with yearly compounding is ln 2 ÷ ln(1 + r):
| Rate | Rule of 72 (years) | Exact (years) | Error |
|---|---|---|---|
| 1% | 72.00 | 69.66 | +3.4% |
| 2% | 36.00 | 35.00 | +2.8% |
| 3% | 24.00 | 23.45 | +2.3% |
| 4% | 18.00 | 17.67 | +1.9% |
| 6% | 12.00 | 11.90 | +0.9% |
| 8% | 9.00 | 9.01 | −0.1% |
| 10% | 7.20 | 7.27 | −1.0% |
| 12% | 6.00 | 6.12 | −1.9% |
| 15% | 4.80 | 4.96 | −3.2% |
| 20% | 3.60 | 3.80 | −5.3% |
At 4% and below, dividing 70 instead of 72 is closer: 70 ÷ 2 = 35.00 matches the exact figure, and 70 ÷ 4 = 17.50 is 0.17 years off where the rule of 72 is 0.33 off. With continuous compounding the exact doubling time is 69.3 ÷ the rate, because ln 2 = 0.693. The rule also works for inflation: at 3% a year, prices double in about 24 years.
Paying in at the start of each period instead of the end gives every contribution one more period of growth, which multiplies the contribution total by (1 + i). For 300 a month at 6% compounded monthly:
| Years | Paid in | End of month | Start of month | Difference |
|---|---|---|---|---|
| 10 | 36,000 | 49,163.80 | 49,409.62 | 245.82 |
| 20 | 72,000 | 138,612.27 | 139,305.33 | 693.06 |
| 30 | 108,000 | 301,354.51 | 302,861.29 | 1,506.77 |
| 40 | 144,000 | 597,447.22 | 600,434.46 | 2,987.24 |
The timing choice is worth 0.5% of the balance at any horizon, since it is one month's growth. The horizon matters far more: interest is 26.8% of the end-of-month balance after 10 years and 75.9% after 40. Frequency matters too. Paying the same 3,600 a year as one lump at each year end grows to 47,826.41 after 10 years, 1,337.40 less than 300 a month, because the monthly payments start earning sooner. Set the timing to when money actually reaches the account: a transfer on the first of each month is a start-of-period payment, and a deduction from pay at month end is an end-of-period one.
For a deposit with no compounding, use the simple interest calculator. To find the monthly amount that reaches a set target, use the savings goal calculator. For monthly mutual fund investments that step up each year, use the SIP calculator.
Checked against: Python decimal (prec 50) of P(1+r/12)^120 + C((1+i)^120−1)/i: 54713.5752536…
Checked against: Microsoft FV documentation, =FV(0.06/12, 10, -200, -500, 1) = $2,581.40; Python decimal gives 2581.40337…
Checked against: 1000·e^0.5 = 1648.7212707… and e^0.05 − 1 = 5.12710964 % (Python decimal exp)
Checked against: 1000 + 24 × 100 by definition
A = P(1 + r/n)^(nt), where P is the deposit, r the annual rate, n the number of compounding periods a year and t the years. 10,000 at 7% compounded monthly for 10 years grows to 10,000 × (1 + 0.07/12)^120 = 20,096.61, so the interest is 10,096.61. Excel's =FV(0.07/12, 120, 0, -10000) returns the same amount.
Less than most people expect. 10,000 at 7% for 10 years grows to 19,671.51 compounded yearly, 20,015.97 quarterly, 20,096.61 monthly, 20,136.18 daily and 20,137.53 continuously. The matching effective annual rates are 7%, 7.1859%, 7.2290%, 7.2501% and 7.2508%, so going from monthly to daily adds about 40 over the decade.
Divide 72 by the annual rate for an estimate (the rule of 72); the exact time with yearly compounding is ln 2 ÷ ln(1 + r). At 7% the rule gives 72 ÷ 7 = 10.29 years and the exact answer is ln 2 ÷ ln 1.07 = 10.24 years. The rule is most accurate near 8%.
Simple interest is paid only on the original deposit; compound interest is also paid on interest already earned. On 10,000 at 7% for 10 years, simple interest is 10,000 × 0.07 × 10 = 7,000, while compounding yearly earns 9,671.51 and compounding monthly earns 10,096.61. The gap widens with time because compound growth is exponential.
A great deal, because the earliest deposits compound the longest. Saving 200 a month at 7% compounded monthly builds 104,185.33 in 20 years from 48,000 of deposits, but 243,994.20 in 30 years from 72,000. The extra 10 years add 24,000 of deposits and 139,808.87 to the final balance.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “10,000 at 7% monthly for 10 years plus 200 a month” is checked against Python decimal (prec 50) of P(1+r/12)^120 + C((1+i)^120−1)/i: 54713.5752536….
Microsoft Excel FV function; U.S. SEC Investor.gov — Compound interest calculator.
For planning only. Lenders, tax authorities and markets apply their own rounding, fees and rules; confirm figures with them before you commit.
6 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
Calculate simple interest (I = P × r × t) and the maturity amount on a principal for a term in years, months or days.
Calculate SIP returns: the maturity value of a monthly mutual fund SIP with an optional yearly step-up, or the SIP needed to reach a goal.
Solve for the future value, present value, interest rate or time of a lump sum from the other three, with any compounding, including continuous.
Calculate how much to save each month to reach a savings goal by a date, or how long a monthly deposit takes to get there, with interest.
Calculate what a purchase will cost after inflation, what your money will still buy, and your real return after inflation.
Calculate CD interest and maturity value from the APY or APR and compounding, convert APY to APR, and see what an early withdrawal penalty costs.
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