How compound interest works
Compound interest is interest paid on the original deposit and on the interest already earned. Each time interest is added, it joins the balance, and the next interest is calculated on that larger balance. Over long periods this snowballs: the interest itself earns interest.
Four things drive the result: the interest rate, how long the money stays in, how often interest is added, and how much you add along the way.
How to use this calculator
The calculator shows what a starting deposit, plus any regular contributions, grows to at a fixed interest rate over a chosen period.
What to enter
- Initial deposit: the amount you start with, in dollars. It can be 0. Default $10,000.
- Annual interest rate: the yearly rate before compounding, from 0% to 100%. Default 5%.
- Investment period: how long the money grows, in whole years from 1 to 100. Default 10.
- Compounding: how often interest is added to the balance (Annually, Twice a year, Quarterly, Monthly, Twice a month, Every two weeks, Weekly, Daily or Continuously). Default Monthly.
- Regular contribution: the amount you add each period, in dollars. Default $0. It is added at the end of each month unless you change that under Advanced options.
Advanced options
The next six fields sit in the Advanced options group. At their defaults they leave the result exactly as it would be without them.
- Contribution frequency: how often the regular contribution is made (Weekly, Every two weeks, Monthly, Quarterly or Yearly), chosen separately from the compounding. Default Monthly.
- Contribution timing: End of each period (the default) or Start of each period, which gives each contribution one more period of interest.
- Additional months: 0 to 11 months added to the period, for a term such as 2 years and 6 months. Default 0.
- Tax on interest: a flat rate from 0% to 60%, taken from the interest each time it is added. Default 0%, no tax.
- Inflation: a yearly rate from 0% to 50%, the same every year. Default 0%, no adjustment.
- Schedule rows: By year (the default) or By month. It changes only the Table tab of the result details and the Download CSV file; the chart stays yearly.
What the results mean
- Final balance: the balance at the end of the period, after tax on interest if a tax rate is set.
- Total deposits: the initial deposit plus every contribution made within the period.
- Interest earned: the final balance minus the total deposits.
- Effective annual rate (APY): how much a balance grows in one full year of compounding, as a percentage. It is the yield before tax and does not depend on the deposits or the period, so it compares rates with different compounding.
- Interest on the initial deposit and Interest on contributions: the interest earned, split by the money that earned it.
- Tax on interest: the total tax taken from the interest over the period.
- Balance in today’s money: the final balance with inflation taken out, at today’s prices.
The last four rows appear only when they are used: the interest split when both the initial deposit and the regular contribution are above 0, the tax row when a tax rate is set, and the balance in today’s money when an inflation rate is set. The worked example below goes through a full calculation, the Math tab of the result details repeats the steps with your own numbers, and “How it’s calculated” lists the formula and its sources.
A worked example with monthly deposits
Suppose you save $100 at the end of every month for 10 years at 6% compounded monthly, starting from nothing. Enter an Initial deposit of 0, an Annual interest rate of 6, an Investment period of 10 and a Regular contribution of 100, and leave the rest as it is.
- Interest is added monthly and deposits are monthly, so the rate per month is 6% ÷ 12 = 0.5%.
- Ten years hold 120 deposits of $100, so Total deposits are $12,000.00.
- Each deposit earns interest from the month after it is made: the first for 119 months, the last for none. Together they grow to a Final balance of $16,387.93.
- Interest earned is $16,387.93 − $12,000.00 = $4,387.93.
With Contribution timing set to Start of each period, every deposit earns one more month of interest, and the same $12,000.00 grows to $16,469.87. With the original settings over 20 years instead, the deposits double to $24,000.00 while the final balance rises to $46,204.09, almost half of it interest.
Simple versus compound interest
Simple interest is paid on the original deposit only, never on earlier interest: I = P·r·t, with P the deposit, r the yearly rate and t the years (LibreTexts, Math for Liberal Arts §8.2). Compound interest adds each interest payment to the balance, so later interest is paid on it too.
Take $10,000 at 5% for 10 years. Simple interest pays $500 a year, $5,000 in all, for a balance of $15,000. Compounded monthly, the same deposit grows to $16,470.09, which is $6,470.09 of interest. The extra $1,470.09 is interest earned on interest, and the gap widens the longer the money stays in.
The effect starts small. $1,000 at 5% compounded once a year becomes $1,050 after one year. In the second year the 5% applies to $1,050, so the balance becomes $1,102.50. Simple interest would give $1,100; the extra $2.50 is interest on the first year’s $50 of interest.
How often interest is added
The more often interest is added, the sooner it earns interest of its own. $10,000 at 5% for 10 years grows to $16,288.95 with annual compounding, $16,470.09 with monthly compounding and $16,486.65 with daily compounding. Each step adds less: annual to monthly adds $181.14, monthly to daily only $16.56.
The effective annual rate (APY) turns any compounding into one yearly figure, so offers with different compounding can be compared directly. At 6% compounded monthly, $1,000 grows to $1,061.68 in a year: $61.68 of interest, an APY of 6.17%.
Tax, inflation and where the interest comes from
With Tax on interest, each interest credit loses the tax share before it is added. $10,000 at 5% compounded monthly for 10 years with a 25% tax grows at 5% × (1 − 0.25) = 3.75% and ends at $14,541.41 instead of $16,470.09. Interest earned is $4,541.41, and the Tax on interest row shows $1,513.80. Together they make $6,055.21, less than the $6,470.09 earned without tax, because money taken as tax no longer earns interest.
With Inflation at 2% a year and no tax, the same $16,470.09 is worth $13,511.21 in today’s money: the final balance divided by 1.02 to the power of 10.
With both an initial deposit and a regular contribution, the interest is split. $10,000 plus $100 a month at 5% compounded monthly for 10 years ends at $31,998.32. Interest on the initial deposit is $6,470.09, exactly what the $10,000 earns on its own, and Interest on contributions is $3,528.23.
The formula
The calculator works one deposit period at a time. With the annual rate R compounded k times a year and contributions made p times a year, the rate per deposit period i and the balance A after n periods are
i = (1 + R / k)^(k / p) − 1
A = P·(1 + i)^n + C·((1 + i)^n − 1) / i
P is the initial deposit and C the contribution at the end of each period; with monthly contributions, i is the equivalent monthly rate. The first term is compound growth, equal to P·(1 + R / k)^(k·t) at every whole year (LibreTexts §8.2). The second is the future value of regular deposits (Olivier, Business Math §11.7, Formula 11.2). Contributions at the start of each period earn one more period of interest each, so the second term is multiplied by (1 + i) (Olivier, Formula 11.3).
For t years and m additional months, n = (12·t + m)·p / 12. When n is not whole, the initial deposit grows for the exact time and only the deposits made inside the term count, as the FAQ shows; this part-period rule is the calculator’s own convention. Total deposits are D = P + C·N for N deposits, and interest earned is I = A − D.
The options use these formulas:
Continuous: A = P·e^(R·t), i = e^(R / p) − 1, APY = e^R − 1
APY: APY = (1 + R / k)^k − 1
Tax: r = R·(1 − T), X = I·T / (1 − T) (X is the "Tax on interest" row)
Today's money: V = A / (1 + f)^t
Interest split: E = P·(1 + i)^n − P, F = I − E
Continuous growth P·e^(R·t) is stated in LibreTexts Math 100 §3.3, and its effective rate e^R − 1 in Sekhon and Bloom, Applied Finite Mathematics §6.2. The APY follows Regulation DD Appendix A (CFPB). With a tax rate T, each credit keeps 1 − T of its interest, so the balance grows at r and the tax is T / (1 − T) of the interest kept. The IRS treats interest as taxable income in the year it becomes available to you (Topic 403); one flat rate taken from each credit is the calculator’s simplification. V divides the balance by the growth of prices at a constant inflation rate f over t years, months included, the way the Federal Reserve Bank of Dallas turns nominal values into real ones. E is what the initial deposit alone earns (LibreTexts §8.2), and F is the rest. Every source is linked under “How it’s calculated”.
FAQ
When are the regular contributions added?
At the end of each period by default. With monthly contributions that is the end of each month, so a contribution starts earning interest the following month. Under Advanced options you can choose Start of each period instead, which gives every contribution one more period of interest, and change how often contributions are made.
What if interest is credited only quarterly or yearly?
Choose Quarterly or Annually under Compounding. How often money goes in is a separate choice, Contribution frequency, so interest can be credited quarterly while deposits are made monthly. Each deposit then earns interest at the equivalent rate for its own period from the moment it is made. A bank that pays nothing on money deposited partway through a crediting period may pay slightly less than the calculator shows.
Does the calculator include tax or inflation?
Yes, as two optional fields under Advanced options, both 0 (off) by default. Tax on interest takes one flat rate that you enter from each interest credit, so the balance and the interest shown are after that tax. It does not look up tax brackets or the rules of particular accounts. Inflation restates the final balance in today's money at one constant yearly rate.
What is continuous compounding?
Interest added at every instant instead of at set intervals, the limit of compounding more and more often. A single deposit grows to A = P·e^(R·t), where e is about 2.71828. It earns only slightly more than daily compounding: $1,000 at 3% for 10 years grows to $1,349.35 compounded monthly, $1,349.84 daily and $1,349.86 continuously. Its effective annual rate is e^R − 1, so 7% compounded continuously has an APY of 7.25%.
What happens when the additional months are not a whole deposit period?
Interest runs to the exact end of the term, but a deposit counts only if it is made inside the term. Take $10,000 plus $300 a quarter at 5% compounded monthly for 2 years and 1 month, which is 8 whole quarters and one month of a ninth. With deposits at the end of each period, 8 are made, for Total deposits of $12,400.00 and a Final balance of $13,614.03. With deposits at the start, the ninth quarter has begun, so 9 are made, giving $12,700.00 and $13,946.89.