Compound Interest Calculator
Future value
$691,150
- Total contributions
- $190,000
- Total interest earned
- $501,150
- Stated rate vs effective annual rate(effective = (1 + r/n)ⁿ − 1)
- 7.00% stated · 7.23% effective
How compounding frequency changes the outcome
$691,150
- Annually
- $642,887 (−$48,263)
- Semiannually
- $668,332 (−$22,819)
- Quarterly
- $681,836 (−$9,314)
- Monthly
- $691,150 (selected)
- Daily
- $695,747 (+$4,597)
Year-by-year growth (30 rows)
| Year | Balance | Cumulative contributions | Interest earned |
|---|---|---|---|
| 1 | $16,919.19 | $16,000 | $919 |
| 2 | $24,338.58 | $22,000 | $2,339 |
| 3 | $32,294.31 | $28,000 | $4,294 |
| 4 | $40,825.16 | $34,000 | $6,825 |
| 5 | $49,972.70 | $40,000 | $9,973 |
| 6 | $59,781.53 | $46,000 | $13,782 |
| 7 | $70,299.43 | $52,000 | $18,299 |
| 8 | $81,577.68 | $58,000 | $23,578 |
| 9 | $93,671.22 | $64,000 | $29,671 |
| 10 | $106,639.02 | $70,000 | $36,639 |
| 11 | $120,544.25 | $76,000 | $44,544 |
| 12 | $135,454.70 | $82,000 | $53,455 |
| 13 | $151,443.02 | $88,000 | $63,443 |
| 14 | $168,587.14 | $94,000 | $74,587 |
| 15 | $186,970.62 | $100,000 | $86,971 |
| 16 | $206,683.03 | $106,000 | $100,683 |
| 17 | $227,820.45 | $112,000 | $115,820 |
| 18 | $250,485.91 | $118,000 | $132,486 |
| 19 | $274,789.85 | $124,000 | $150,790 |
| 20 | $300,850.72 | $130,000 | $170,851 |
| 21 | $328,795.53 | $136,000 | $192,796 |
| 22 | $358,760.48 | $142,000 | $216,760 |
| 23 | $390,891.60 | $148,000 | $242,892 |
| 24 | $425,345.48 | $154,000 | $271,345 |
| 25 | $462,290.03 | $160,000 | $302,290 |
| 26 | $501,905.30 | $166,000 | $335,905 |
| 27 | $544,384.37 | $172,000 | $372,384 |
| 28 | $589,934.26 | $178,000 | $411,934 |
| 29 | $638,776.94 | $184,000 | $454,777 |
| 30 | $691,150.47 | $190,000 | $501,150 |
Estimates only. Assumes a fixed contribution each month and a fixed rate — actual investment returns vary year to year. Inflation, taxes on gains, and account fees are not modeled here.
Compound interest makes your money earn money — each interest payment joins the principal, and next period's interest is computed on the new, larger balance. On $10,000 invested at 7% with $500 a month added for 30 years, the future value lands near $691,150 — $190,000 contributed and $501,150 earned as interest. The same cash flow at simple interest (earnings never reinvested) reaches only $211,000, a gap of $480,150. Compounding frequency matters far less than the marketing implies: moving from annual to daily compounding is worth about 7.6% of the final balance, and daily over monthly barely registers at 0.7% — the contribution, the rate, and the time horizon drive almost all of the growth.
What compounding does to a balance
There are two ways for a savings balance to grow. Simple interest pays interest on the original principal only — $1,000 at 5% pays $50 a year, every year. Compound interest adds the interest to the principal, so next year's interest is computed on $1,050, not $1,000. Over enough time, compounding produces a steep curve:
- Year 1: $1,000 → $1,050
- Year 10: $1,000 → $1,629
- Year 30: $1,000 → $4,322
- Year 50: $1,000 → $11,467
This is the math behind savings accounts, CDs, and bond ladders — and, scaled up with monthly contributions, behind retirement savings.
The textbook formula for a lump sum is:
FV = P × (1 + r/n)^(n × t)
where P is the principal, r is the annual rate, n is the number of compounding periods per year, and t is the time in years. Add a contribution each period and you get the standard annuity-on-compound formula. The calculator above runs the same math by direct simulation, period by period, to keep contributions and compounding frequency aligned.
What moves the future value
- Initial principal. Doubling the starting deposit doubles the lump-sum growth — and the added interest compounds too.
- Monthly contribution. Past the first year, what you add each month matters more than where you started. A regular $500 a month for 30 years dwarfs a $50,000 starting balance on its own.
- Annual rate. Higher rates help; the future value scales non-linearly with rate because of compounding. On a 30-year $10K + $500/mo plan: $460,807 at 5%, $562,483 at 6%, and $691,150 at 7% — each additional point is worth more than the last (+$101,676, then +$128,667).
- Time horizon. Doubling the time more than doubles the future value on a contributing plan, again because each year's contribution is itself compounding.
- Compounding frequency. Among the five common cadences (annual, semiannual, quarterly, monthly, daily), most of the variation sits between annual and monthly. Daily vs monthly moves the result by less than 0.1% of principal — a real but small effect. The "compounding frequency table" in the calculator shows the dollar difference for your numbers.
Effective annual rate: what the stated rate leaves out
A savings account quoting 7% APY and a CD quoting 7% APR compounded monthly are not the same. The APY (annual percentage yield) already reflects compounding; the APR compounded monthly delivers 7% × (1 + 7%/12)^12 − 1 = 7.229% as the equivalent effective annual rate.
The difference is small at modest rates and bigger at higher rates:
| Stated rate | Monthly effective annual rate |
|---|---|
| 1% | 1.005% |
| 5% | 5.116% |
| 7% | 7.229% |
| 10% | 10.471% |
| 15% | 16.075% |
The headline rate your bank or broker advertises is usually APY for this reason — it lets you compare across products without recalculating. Investments priced by simple APR need an adjustment like the table above.
How to use this calculator
The page opens with $10,000 initial, $500 a month, 7% over 30 years at monthly compounding:
- Adjust Initial deposit to your starting point. Enter zero if you are starting from scratch and testing the contribution alone.
- Set the Monthly contribution you can sustain — and try variations like "$250 a month for 30 years" vs "$500 a month for 25 years" to compare real scenarios.
- Set the Annual interest rate to a reasonable long-run assumption. A common long-run stock market assumption is 7% real, ~10% nominal pre-inflation. Adjust for the asset class you are modeling.
- Pick the Time horizon that matches your goal — 30 years for retirement, 5–10 for a down payment fund.
- Choose a Compounding frequency to model. Monthly is the practical default; switching to Daily is mostly a sanity check that the differences are minor.
- Read results: Future value, Total contributions, Total interest earned, then the Compounding frequency comparison card showing the same inputs at all five frequencies and the Year-by-year growth table.
Compound interest FAQ
How does compound interest work?
Each period, the bank or fund adds the accrued interest to your balance. Next period's interest is calculated on the new, larger balance. Over time, this produces exponential growth that simple interest cannot match. Most bank products (savings, money market, CDs) compound monthly or daily; bonds compound semiannually; many student loans compound daily. The math is the same regardless of cadence.
What is the rule of 72?
A back-of-envelope rule for how long it takes to double: years to double = 72 / rate (in %). At 7%, doubling takes roughly 10.3 years; at 10%, about 7.2. It is approximate (off by 1-2% at typical rates) but fast to run in your head.
How often does a savings account compound?
Most online savings accounts compound daily but pay interest monthly — they credit accrued interest once a month. CDs commonly compound daily or monthly; money market funds usually compound daily and pay out dividends monthly. The calculator's Compounding frequency menu covers all of these.
Do I pay taxes on compound interest?
In a taxable account, yes — interest income is taxed in the year it is paid out, even if you reinvest it. In tax-advantaged accounts (401(k), IRA, HSA, 529), the growth compounds tax-deferred. The calculator shows gross growth only; taxes depend on the wrapper and your bracket.
How fast does $1,000 grow at 5% interest compounded monthly?
After 10 years, about $1,647. After 30 years, about $4,468. After 50 years, about $12,119. Doubling time at 5% is roughly 14 years, so the $1,000 becomes about $2,011 by year 14, $4,043 by year 28, and $8,131 by year 42.
What is the difference between APR and APY?
APR (annual percentage rate) is the stated rate without compounding. APY (annual percentage yield) bakes in compounding and represents the true one-year return. At the same nominal rate, APY is always higher than APR for any frequency above annual. US bank deposit disclosures are required by regulation to quote APY so consumers can compare products on a like-for-like basis.
Are mutual funds compound interest?
A mutual fund's net asset value reflects whatever the underlying holdings have produced, with reinvested distributions. If the fund reinvests dividends and capital gains (the default for most retirement accounts), your share of the growth compounds. The future value on this page describes that compounding, although in practice fund returns are volatile rather than smooth.
Sources: The compounding math (FV = P × (1 + r/n)^(n×t)) is the standard textbook formula, used identically by financial institutions, internal revenue service account projections, and the SEC's compound interest calculator. APY comparisons reflect Regulation DD truth-in-savings rules (12 CFR § 1030). The calculator does not model inflation, taxes, or product fees — all three matter for a real projection, and contribute to the gap between any back-of-envelope forecast and actual account growth.
Disclaimer: This calculator is for informational and educational purposes only and is not investment advice. Actual returns vary year to year, and past performance is not a guarantee of future results. Inflation and taxes can substantially reduce the real future value shown here.