Reading the sample run
Load sample fills in $10,000 at 7% a year, compounded monthly, for 20 years, with $200 deposited at the end of every month. The balance lands at $144,572.72.
- $58,000 of the balance is your money: the $10,000 start plus 240 deposits of $200.
- $86,572.72 is interest. By year 20 the interest outweighs everything you deposited.
- $80,046.41 is the same balance in today's dollars at 3% inflation. Close to half the headline number disappears once prices rise for two decades.
Look at the year column in the table. The balance reaches $54,714 at year 10 and $144,573 at year 20. The second decade adds about twice what the first one did, with the same $200 a month going in. Interest earned on earlier interest drives the gap.
Switch the timing to start of each period and the result rises to $145,180.47. Each deposit gets one extra month of growth, worth about $600 over 20 years. Small, but a free gain if your pay date lets you deposit on the 1st.
The future value formula, in two parts
The calculator adds two separate pieces: what the starting balance grows into, and what the stream of deposits grows into.
lump sum: FV = PV × (1 + r/n)^(n × t)
deposits: FV = PMT × ((1 + i)^(p × t) - 1) / i
start-of-period deposits: multiply the deposit part by (1 + i)Here r is the yearly rate as a decimal, n is compounding periods per year, t is years, and p is deposits per year. i is the rate per deposit period. When deposits and compounding line up, monthly and monthly for example, i is r/12. When they differ, the calculator converts with i = (1 + r/n)^(n/p) - 1, so a quarterly-compounding account with monthly deposits still gets the right answer.
Continuous compounding swaps (1 + r/n)^(n × t) for e^(r × t). At a 0% rate the formula breaks, since i sits under the division line, so the tool falls back to adding up the deposits.
Does compounding frequency matter?
Less than most bank ads suggest. Here is $10,000 at 6% for 10 years with no deposits:
| Compounding | Balance | Gain over yearly |
|---|---|---|
| Yearly | $17,908.48 | - |
| Quarterly | $18,140.18 | $231.70 |
| Monthly | $18,193.97 | $285.49 |
| Daily | $18,220.29 | $311.81 |
| Continuously | $18,221.19 | $312.71 |
Going from yearly to monthly is worth about $285. Going from daily to continuous is worth 90 cents. When you compare two savings accounts, check the APY, the effective yearly rate shown in the results panel, instead of the compounding schedule. A 5.0% APY beats a 4.8% rate compounded daily, which works out to a 4.92% APY.
Starting earlier vs depositing more
Three savers, all earning 7% compounded monthly, no starting balance:
| Plan | Total deposited | Balance |
|---|---|---|
| $300 a month for 30 years | $108,000 | $365,991 |
| $300 a month for 20 years | $72,000 | $156,278 |
| $450 a month for 20 years | $108,000 | $234,417 |
The first and third savers deposit the same $108,000. The one who started ten years earlier ends with about $131,600 more. If you are deciding between waiting for a raise to save more and starting with a smaller amount now, the numbers favor now.
Where a future value number goes wrong
- Markets do not pay a flat rate. A 7% stock return is an average over decades with losing years mixed in. The calculator applies 7% every single year, so the year-by-year path is smoother than anything you will see in a brokerage account, and the end figure is a midpoint, not a promise. For a savings account or CD with a fixed rate, the result is close to exact.
- Fees compound too. $500 a month for 30 years at 7% reaches $609,986. Knock 1% off for a fund fee and the result drops to $502,258. Enter your rate after fees.
- Taxes are not modeled. Interest in a taxable account loses a slice every year. Use an after-tax rate for those, and the full rate for a 401(k), IRA, or ISA where growth is sheltered.
- Deposits stay fixed. Most people raise their savings as pay rises. The tool keeps the deposit flat for the whole term, so a plan with yearly increases ends higher than the number shown here.
- No withdrawals. The model only adds money. For a plan where you draw income in later years, the FIRE calculator or the annuity calculator fits better.