What is the compound interest formula?

A = P(1 + r/n)^(nt), where P is the initial deposit, r the annual rate as a decimal, n the number of compounding periods a year and t the years. With continuous compounding it is A = Pe^(rt). For $10,000.00 at 5% compounded monthly for 10 years, A = $16,470.09.

How are regular contributions handled?

They use the future value of an annuity, FV = PMT × ((1+i)^k − 1) / i, where i is the effective rate per contribution period and k the number of contributions. For an annuity due (paid at the start of each period) the result is multiplied by 1+i. In the example, $200.00 a month at the end of the month adds up to $24,000.00 in deposits and $47,526.55 in total; paying at the start of the month instead gives $47,655.95.

What if contributions and compounding happen at different frequencies?

The calculator uses the effective rate per contribution period, so each deposit earns exactly what the compounding rule says it should. With 6% compounded annually, a monthly deposit earns 1.06^(1/12) − 1 = 0.486755% a month, not 6% ÷ 12 = 0.5%. With the example's monthly compounding and monthly deposits it is 0.416667% a month, and a yearly deposit earns the APY, 5.1162%. Money added part-way through a compounding period therefore earns a proportional share of that period's interest.

What is the effective annual yield (APY)?

APY is the interest you actually earn in one year once compounding is counted: (1 + r/n)^n − 1, or e^r − 1 when compounding is continuous. A 5% rate compounded monthly has an APY of 5.1162%; compounded annually it is exactly 5%.

Does compounding more often make a big difference?

Less than most people expect. For $10,000.00 at 5% over 10 years the balance is $16,288.95 compounded annually, $16,470.09 monthly and $16,487.21 continuously. The rate and the time matter far more.

Is the beginning or end of the period better?

Beginning is better because each deposit earns interest for one more period. In the example, deposits at the start of each month finish at $47,655.95 against $47,526.55 at the end of each month, with the same $34,000.00 contributed.

How much comes from contributions and how much from interest?

In the example $34,000.00 is your own money and $13,526.55 is interest. Without the monthly deposits the initial $10,000.00 alone would grow to $16,470.09. The year-by-year table shows how the interest share grows over time.

Does this account for taxes, fees or inflation?

No. It shows nominal growth at a fixed rate. Taxes, account fees, changing rates and inflation would all lower what you actually keep or can buy, so treat the result as an estimate, not financial advice.

Is anything I type stored or sent?

No. The calculation runs in your browser and nothing you enter leaves your device.

Compound Interest Calculator

$10,000.00 at 5% compounded monthly for 10 years, with $200.00 added at the end of every month, grows to $47,526.55: $34,000.00 of your own money plus $13,526.55 of interest, an effective annual yield (APY) of 5.1162%. Enter an initial deposit, the annual rate, how often interest compounds (annually, semiannually, quarterly, monthly, daily or continuously) and the time in years and months. Add a regular monthly or yearly contribution if you like, paid at the beginning or end of each period. It uses A = P(1 + r/n)^(nt), A = Pe^(rt) for continuous compounding and the future value of an annuity for the contributions, and shows the final balance, total contributions, total interest, APY and a year-by-year table. This is an estimate for planning, not financial advice.

Updated 2026-10-11Runs in your browser: nothing you enter is uploadedHow this tool works

Final balance $47,526.55

$34,000.00 contributed and $13,526.55 interest over 10 years.

Final balance: $47,526.55
Initial deposit: $10,000.00
Regular contributions: $24,000.00
Total contributions: $34,000.00
Total interest: $13,526.55
Effective annual yield (APY): 5.1162%
Effective rate per month: 0.416667%

An estimate for planning, not financial advice.

Year-by-year balance

Totals at the end of each year. Contributions include the initial deposit.

Year	Total contributions	Total interest	Balance
1	$12,400.00	$567.39	$12,967.39
2	$14,800.00	$1,286.60	$16,086.60
3	$17,200.00	$2,165.39	$19,365.39
4	$19,600.00	$3,211.93	$22,811.93
5	$22,000.00	$4,434.80	$26,434.80
6	$24,400.00	$5,843.03	$30,243.03
7	$26,800.00	$7,446.09	$34,246.09
8	$29,200.00	$9,253.96	$38,453.96
9	$31,600.00	$11,277.11	$42,877.11
10	$34,000.00	$13,526.55	$47,526.55

How compounding frequency changes $10,000.00 at 5% over 10 years

Same rate and time, no contributions. More frequent compounding raises the APY a little.
Compounding	APY	Balance after 10 years	Interest earned
Annually	5%	$16,288.95	$6,288.95
Semiannually	5.0625%	$16,386.16	$6,386.16
Quarterly	5.0945%	$16,436.19	$6,436.19
Monthly	5.1162%	$16,470.09	$6,470.09
Daily (365)	5.1267%	$16,486.65	$6,486.65
Continuously	5.1271%	$16,487.21	$6,487.21

Growth of $1,000.00 compounded annually

Each cell is the balance after that many years with no contributions.
Annual rate	10 years	20 years	30 years
3%	$1,343.92	$1,806.11	$2,427.26
5%	$1,628.89	$2,653.30	$4,321.94
7%	$1,967.15	$3,869.68	$7,612.26
10%	$2,593.74	$6,727.50	$17,449.40

Contribution timing and frequency in the example

$10,000.00 at 5% compounded monthly for 10 years, with $200.00 added at the end of every month, with the contribution changed one way at a time.
Contribution	Total contributions	Total interest	Final balance
None	$10,000.00	$6,470.09	$16,470.09
$200.00 monthly, end of month	$34,000.00	$13,526.55	$47,526.55
$200.00 monthly, start of month	$34,000.00	$13,655.95	$47,655.95
$2,400.00 yearly, end of year	$34,000.00	$12,821.25	$46,821.25

How to calculate compound interest and future value

Enter the initial deposit. Type the amount you start with. The example is $10,000.00; it can be 0.
Enter the annual interest rate. Use the nominal yearly rate as a percentage, such as 5.
Choose how often interest compounds. Pick annually, semiannually, quarterly, monthly, daily (365) or continuously. Your bank or account terms say which applies.
Set the time. Enter whole years and extra months, up to 100 years in total. The example uses 10 years.
Add regular contributions (optional). Enter an amount, choose monthly or yearly, and say whether it is paid at the beginning or end of each period. The example adds $200.00 at the end of every month.
Read the result. The example reaches $47,526.55, with $13,526.55 of interest and an APY of 5.1162%. Scroll to the year-by-year table for the balance at the end of each year.

Frequently asked questions

What is the compound interest formula?: A = P(1 + r/n)^(nt), where P is the initial deposit, r the annual rate as a decimal, n the number of compounding periods a year and t the years. With continuous compounding it is A = Pe^(rt). For $10,000.00 at 5% compounded monthly for 10 years, A = $16,470.09.
How are regular contributions handled?: They use the future value of an annuity, FV = PMT × ((1+i)^k − 1) / i, where i is the effective rate per contribution period and k the number of contributions. For an annuity due (paid at the start of each period) the result is multiplied by 1+i. In the example, $200.00 a month at the end of the month adds up to $24,000.00 in deposits and $47,526.55 in total; paying at the start of the month instead gives $47,655.95.
What if contributions and compounding happen at different frequencies?: The calculator uses the effective rate per contribution period, so each deposit earns exactly what the compounding rule says it should. With 6% compounded annually, a monthly deposit earns 1.06^(1/12) − 1 = 0.486755% a month, not 6% ÷ 12 = 0.5%. With the example's monthly compounding and monthly deposits it is 0.416667% a month, and a yearly deposit earns the APY, 5.1162%. Money added part-way through a compounding period therefore earns a proportional share of that period's interest.
What is the effective annual yield (APY)?: APY is the interest you actually earn in one year once compounding is counted: (1 + r/n)^n − 1, or e^r − 1 when compounding is continuous. A 5% rate compounded monthly has an APY of 5.1162%; compounded annually it is exactly 5%.
Does compounding more often make a big difference?: Less than most people expect. For $10,000.00 at 5% over 10 years the balance is $16,288.95 compounded annually, $16,470.09 monthly and $16,487.21 continuously. The rate and the time matter far more.
Is the beginning or end of the period better?: Beginning is better because each deposit earns interest for one more period. In the example, deposits at the start of each month finish at $47,655.95 against $47,526.55 at the end of each month, with the same $34,000.00 contributed.
How much comes from contributions and how much from interest?: In the example $34,000.00 is your own money and $13,526.55 is interest. Without the monthly deposits the initial $10,000.00 alone would grow to $16,470.09. The year-by-year table shows how the interest share grows over time.
Does this account for taxes, fees or inflation?: No. It shows nominal growth at a fixed rate. Taxes, account fees, changing rates and inflation would all lower what you actually keep or can buy, so treat the result as an estimate, not financial advice.
Is anything I type stored or sent?: No. The calculation runs in your browser and nothing you enter leaves your device.

How it works

With no contributions the balance is A = P(1 + r/n)^(nt) for n compounding periods a year, or A = Pe^(rt) for continuous compounding, where t may be fractional (years plus months ÷ 12). To handle contributions at any frequency the calculator advances month by month with the exact monthly growth factor g = (1 + r/n)^(n/12), or e^(r/12) when continuous; that is the same curve as the formula above at every month, so the result matches it exactly. A monthly contribution then earns the effective rate i = g − 1 per period and a yearly one i = g^12 − 1, the APY, which is the effective rate per contribution period. A contribution at the end of a period is added after that period’s growth, one at the beginning before it, giving the ordinary annuity and annuity-due formulas; the unit tests check the month-by-month result against both closed forms. Yearly contributions are made at month 12, 24 and so on (end) or months 1, 13 and so on (beginning), so a final partial year gets a beginning contribution but no end contribution. Calculations use ordinary floating-point numbers and are rounded to the cent only for display, so a displayed total can differ by a cent from adding the displayed parts. Interest is shown as the balance minus everything deposited. Real accounts may differ in how they credit interest, count days, and round each period, and rates, taxes, fees and inflation are not modelled. This is an estimate for planning and not financial advice. Everything runs in your browser and nothing you type is sent anywhere.

Sources

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