How to use the compound interest calculator
Start with the money you have now, then add what you plan to deposit each month. Keep the two apart. The starting amount grows for the whole term, while each deposit only grows from the month it goes in.
Use the rate and compounding schedule from your account terms. If the bank only quotes an APY, pick annual compounding so the yield isn't compounded twice.
- Enter your starting amount and your monthly contribution.
- Choose whether deposits land at the beginning or end of each month.
- Add a yearly change to the deposit if you plan to raise it (for example 3% a year).
- Enter the annual rate and pick daily, monthly, quarterly, semiannual or annual compounding.
- Set the years plus any extra months, then add a fee, an inflation guess and a target if you want them.
- Read the ending balance, the split between money you put in and growth, and the yearly table.
Compound interest formula with monthly contributions
For a lump sum, the compound interest formula is A = P(1 + r/n)^(nt). P is the principal, r is the annual rate as a decimal, n is compounding periods per year and t is years. Monthly deposits add a second piece, because each deposit sits in the account for a different number of months.
When deposits and compounding are both monthly, the deposit piece is a future value of annuity formula. With $5,000 up front, $200 a month, 7% and 10 years, the lump sum grows to $10,048.31 and the deposits grow to $34,616.96. Together that's $44,665.27, the same answer the calculator gives.
For other schedules, the calculator turns your rate and compounding choice into an equal monthly growth factor, then steps through every month. Deposits at the start of a month get that month's growth. Deposits at the end don't.
Lump sum: A = P x (1 + r / n)^(n x t)Monthly deposits (end of month): FV = PMT x ((1 + i)^N - 1) / i, where i = r / 12 and N = monthsMonthly deposits (start of month): multiply the line above by (1 + i)Monthly growth factor for any schedule = (1 + r / n)^(n / 12)APY = (1 + r / n)^n - 1Inflation-adjusted value = ending balance / (1 + inflation)^t
Example: $5,000 plus $200 a month at 7%
Put in $5,000, add $200 at the end of every month, and assume 7% compounded monthly for 10 years. You end with $44,665.27. You supplied $29,000 of that yourself, so $15,665.27 is growth.
With 2.5% yearly inflation, that balance buys about what $34,892.44 buys today. Moving each deposit to the start of the month raises the ending balance to $44,867.20, or $201.93 more.
| Years | Money you put in | Growth | Ending balance |
|---|---|---|---|
| 5 | $17,000.00 | $4,406.71 | $21,406.71 |
| 10 | $29,000.00 | $15,665.27 | $44,665.27 |
| 20 | $53,000.00 | $71,379.03 | $124,379.03 |
| 30 | $77,000.00 | $207,576.69 | $284,576.69 |
Daily compound interest vs monthly
Daily compounding adds interest 365 times a year, so it earns a little more than monthly at the same stated rate. A little is the key word. $10,000 at 5% for one year ends at $10,512.67 with daily compounding and $10,511.62 with monthly. That's a $1.05 difference, and the APY moves from 5.12% to 5.13%.
With regular deposits the gap stays small. The table keeps the $5,000 start, $200 a month, 7% rate and 10 years, and changes only the schedule. Daily beats monthly by $57.49. Adding one more year or a slightly higher deposit matters far more.
| Compounding | APY | Ending balance | More than annual |
|---|---|---|---|
| Annually | 7.00% | $44,046.10 | $0.00 |
| Semiannually | 7.12% | $44,376.15 | $330.05 |
| Quarterly | 7.19% | $44,548.01 | $501.91 |
| Monthly | 7.23% | $44,665.27 | $619.17 |
| Daily | 7.25% | $44,722.76 | $676.66 |
Raising your monthly contributions each year
The annual change field raises (or lowers) your monthly deposit after each full year. It's a simple way to model saving part of every raise. Keep the rest of the example the same and a 2% yearly increase adds $2,860.16 by year 10. A 5% increase adds $7,721.91.
If you enter a target, the calculator also solves for the starting monthly deposit that reaches it. To hit $50,000 in the example, you'd need $230.82 a month instead of $200.
| Yearly increase | Money you put in | Ending balance | Gain over flat deposits |
|---|---|---|---|
| 0% | $29,000.00 | $44,665.27 | $0.00 |
| 2% | $31,279.33 | $47,525.43 | $2,860.16 |
| 5% | $35,186.94 | $52,387.18 | $7,721.91 |
How fees shrink compound growth
A yearly fee comes out of the balance, and the money it removes stops compounding too. Investor.gov warns that small ongoing fees add up over long periods. The calculator spreads your percentage fee across the months and shows the gap against a no-fee run.
This example starts at $10,000, adds $300 a month at 7% for 20 years. A 1% fee costs $25,191.86, about 12.8% of the ending balance.
| Annual fee | Ending balance | Fee drag | Lower than no fee |
|---|---|---|---|
| 0% | $196,665.39 | $0.00 | 0.00% |
| 0.25% | $190,002.59 | $6,662.80 | 3.39% |
| 0.50% | $183,589.27 | $13,076.11 | 6.65% |
| 1.00% | $171,473.53 | $25,191.86 | 12.81% |
When to double-check the result
This is a steady-rate projection. Savings rates change, and investments can lose value, so a 7% input is an assumption you choose. Use the sensitivity range to see a lower and higher rate side by side. In the main example, 5% and 9% give $39,291.50 and $50,959.64.
The calculator leaves out taxes, withdrawals, one-time charges, employer matches and contribution limits. Banks may also credit interest on daily balances or statement dates that don't line up with a monthly model. Check the account disclosure before you rely on a number for a real decision.
Sources
These public references back up the formula, the APY rules, the fee warning and the inflation adjustment on this page.