Compound Interest Calculator
Enter a starting amount, an interest rate, a time and how often interest compounds — add regular deposits if you like — and get the future value, the interest earned and a year-by-year table with a growth chart. The working is written out so you can check it against a textbook or spreadsheet. Free, no sign-up.
Your numbers
Interest rate is a nominal annual rate; the balance grows by (1 + rate ÷ m) each compounding period.
Results
$50,969.84
Future value
$34,000.00
Total you put in
$16,969.84
Interest earned
6.1678%
Effective annual rate (APY)
The working
Starting amount: 10,000.00 × (1 + 0.06 ÷ 12)^(12 × 10) = 18,193.97
120 deposits of 200.00, grown to the end of the term = 32,775.87
Future value: 18,193.97 + 32,775.87 = 50,969.84
Effective annual rate: (1 + 0.06 ÷ 12)^12 − 1 = 6.167781%
Year by year
| Year | Deposits | Interest | Total put in | Balance |
|---|---|---|---|---|
| 1 | $2,400.00 | $683.89 | $12,400.00 | $13,083.89 |
| 2 | $2,400.00 | $874.10 | $14,800.00 | $16,357.99 |
| 3 | $2,400.00 | $1,076.04 | $17,200.00 | $19,834.03 |
| 4 | $2,400.00 | $1,290.43 | $19,600.00 | $23,524.46 |
| 5 | $2,400.00 | $1,518.05 | $22,000.00 | $27,442.51 |
| 6 | $2,400.00 | $1,759.71 | $24,400.00 | $31,602.21 |
| 7 | $2,400.00 | $2,016.27 | $26,800.00 | $36,018.48 |
| 8 | $2,400.00 | $2,288.65 | $29,200.00 | $40,707.14 |
| 9 | $2,400.00 | $2,577.84 | $31,600.00 | $45,684.97 |
| 10 | $2,400.00 | $2,884.86 | $34,000.00 | $50,969.84 |
How to Use the Compound Interest Calculator
- 1. Pick a currency. The amounts are formatted for the currency you choose and your language. Choose No currency to see plain numbers.
- 2. Enter the balance, rate and time. The rate is a nominal annual rate — the figure a bank quotes before compounding. Time is in years; use 2.5 for two and a half.
- 3. Choose how interest compounds. From annually to daily, or continuously. This changes the result more than most people expect at high rates and long terms.
- 4. Add deposits (optional). Enter the amount, how often it is paid in, and whether each deposit lands at the start or the end of its period. Leave it at 0 to compound the starting amount alone.
- 5. Read the results. The future value, the total you put in, the interest earned and the effective annual rate appear above a chart and a year-by-year table.
The Compound Interest Formula
With a starting amount P, a nominal annual rate r, n compounding periods per year and t years, the balance becomes A = P(1 + r/n)nt. Each period the balance is multiplied by 1 + r/n, and the interest from earlier periods earns interest itself — that is what separates compound from simple interest. For continuous compounding the limit is A = Pert.
Regular deposits of size D add the future value of an annuity. If the deposits fall on the compounding dates and are paid at the end of each period, they grow to D × ((1 + i)N − 1) ÷ i, where i = r/n is the rate per period and N is the number of deposits. Paying at the start of each period (an annuity due) multiplies that by 1 + i. These are the same conventions Excel uses for its FV function, and the calculator is tested against Excel's documented examples.
The convention used here
Between deposit dates the balance grows by the equivalent rate, (1 + r/n)n × t, with t measured in years. When deposits fall on the compounding dates this is exactly the textbook formula. If you deposit monthly into an account that compounds annually, a bank that credits interest only once a year would show a slightly lower balance than this calculator, so treat that case as an estimate.
Worked Example
Start with 10,000 at 6% compounded monthly for 10 years. The monthly rate is 0.06 ÷ 12 = 0.005 and there are 120 periods, so the starting amount grows to 10,000 × 1.005120 = 18,193.97 — an interest gain of 8,193.97.
Now add 200 at the end of every month. The deposits total 24,000 and grow to 200 × (1.005120 − 1) ÷ 0.005 = 32,775.87. The future value is 18,193.97 + 32,775.87 = 50,969.84. Of that, 34,000 is money you put in and 16,969.84 is interest. Putting the deposits at the start of each month instead lifts the result to 51,133.72.
| Compounding (10,000 at 6% for 10 years) | Future value |
|---|---|
| Annually | 17,908.48 |
| Quarterly | 18,140.18 |
| Monthly | 18,193.97 |
| Daily (365) | 18,220.29 |
More frequent compounding always helps, but with diminishing returns: going from annual to monthly adds 285 here, while going from monthly to daily adds only 26. The time you leave the money and the rate matter far more than the compounding schedule.
Reading the Table and Chart
- Deposits is what you paid in during that year; Interest is what the balance earned in that year, so each year's interest is larger than the last when you keep the money in.
- Total put in is the starting amount plus every deposit so far — the gap between it and the balance is the interest earned to date.
- The effective annual rate (APY) is the rate that, compounded once a year, gives the same growth as your nominal rate does at your compounding frequency. 6% compounded monthly is an APY of 6.1678%. The APR to APY Converter does this on its own.
- The chart starts at zero so that the interest does not look bigger than it is; download it as SVG or PNG for a report.
What This Calculator Leaves Out
It models a fixed rate with no withdrawals. Real returns vary, fees reduce them, taxes may apply to the interest, and inflation lowers what the future value will buy. It is an educational calculator for coursework and for understanding how the formula behaves, not financial advice and not a forecast of any product's return.
Frequently Asked Questions
- What is the formula for compound interest?
- A = P(1 + r/n)nt, where P is the starting amount, r the nominal annual rate as a decimal, n the number of compounding periods per year and t the time in years. The interest earned is A − P. For continuous compounding use A = Pert.
- How do I calculate compound interest with monthly contributions?
- Grow the starting amount with the formula above, then add the future value of the deposits: D × ((1 + i)N − 1) ÷ i, with i = r ÷ 12 and N the number of months. This calculator does both parts and shows the working. For deposits at the start of each month, multiply the deposit part by 1 + i.
- Does it matter whether interest compounds daily or monthly?
- Slightly. For 10,000 at 6% over 10 years, monthly compounding gives 18,193.97 and daily gives 18,220.29 — a difference of about 26. The gap grows with higher rates and longer terms, but the rate and the number of years matter much more.
- What is the difference between compound and simple interest?
- Simple interest is calculated on the original amount only, so it grows by the same amount every period. Compound interest is calculated on the balance including past interest, so growth accelerates. Compare them in the Simple Interest Calculator.
- What is the rule of 72?
- A shortcut: divide 72 by the annual percentage rate to estimate the years needed to double your money. At 6% that is 72 ÷ 6 = 12 years. The exact figure for 6% compounded monthly is about 11.6 years, so the rule is a quick estimate, not a result.
- What is the difference between APR and APY?
- APR here is the nominal annual rate; APY is the effective annual rate after compounding. A 6% rate compounded monthly has an APY of 6.1678%. Lenders and banks may define APR and APY under their own regulations, so for a real product use the figures it discloses.