Compound Interest Calculator
Project compound growth with contributions, compare effective rates, CAGR and the rule of 72, and solve for term, principal or rate
① 本金 + 定投，最后能变成多少
② 复合年化增长率（CAGR）与翻倍时间
③ 反推：要多久、要多少本金、要多高收益
填写任意一张卡片的参数即可自动计算，三张卡片互相独立，不需要点击按钮
About this tool
The compound interest formula fits on one line. The part that goes wrong is the conventions: nominal or effective rate, contributions at the start or end of each period, and what exactly is being compared against simple interest. This tool separates the three questions, and each card works on its own:
- Future value and yearly detail: starting principal plus recurring contributions, compounding by year, quarter or month, with annual contributions, interest, year-end balance and cumulative return, alongside the simple-interest result so the contribution of interest on interest is visible
- Rate conversion: periodic rate, nominal annual rate and effective annual rate together, with a table comparing annual, semi-annual, quarterly, monthly, daily and continuous compounding, so the same 10,000 over 10 years can be compared side by side
- Growth and doubling: CAGR from the first and last values and the number of years, years needed to double and triple, checked against the rule of 72 and the rule of 69.3 with the error in days shown
- Three reverse questions: how long, how much principal, and what rate, all solved with the same formula and each result verified by substitution
When to use it
- Recurring investments: what a fixed monthly contribution grows to over the years
- Education and retirement funds: working back from a target to the monthly saving and return required
- Comparing products: 4% nominal compounded monthly against 4.1% effective, and the real gap
- Checking marketing claims: the annual return implied by doubling in three years, and how far the rule of 72 misses
- Long-term track record: turning a move from 0.5 to 1.2 over six years into an annual rate
Formulas used
| Item | Formula | Example (100,000 principal plus 3,000 monthly, 4% nominal compounded monthly, 20 years) |
|---|---|---|
| Compound future value | FV = P x (1 + r/m)^(m x n) | Principal portion 222,258.21 |
| Annuity future value | FV = A x ((1 + i)^N - 1) / i | Contribution portion 1,100,323.88 |
| Total | Principal plus annuity future value | 1,322,582.09, on 820,000 contributed, a gain of 502,582.09 or 61.29% |
| Beginning-of-period contributions | Annuity part multiplied by (1 + i) | 1,326,249.83, which is 3,667.75 more than end-of-period |
| Effective annual rate | EAR = (1 + r/m)^m - 1 | 4% nominal monthly gives an EAR of 4.0742% |
| Simple interest | Only principal earns interest | 1,186,800.00, so compounding adds 135,782.09 |
| CAGR | (end / start)^(1 / n) - 1 | 50 to 120 over 6 years gives 15.709% |
| Doubling time | ln2 / ln(1 + g); rule of 72 uses 72 / percentage | Exact 4.75 years, rule of 72 gives 4.58, short by 61.1 days |
Three reverse examples
- How long: 50,000 principal, 2,000 monthly, 5% annual rate, target 1,000,000. Reached in month 247, or 20.58 years; planning in whole years gives 21 years and 1,031,254.78
- How much principal: 2,000 monthly, 6% annual rate, target 1,000,000 in 12 years. You need 282,676.80 today
- What rate: 50,000 principal, 2,000 monthly, target 1,000,000 in 15 years. You need a nominal rate of 9.513%, an effective rate of 9.939%; at 3% the same plan reaches only 532,316.97
FAQ
- What is the difference between simple and compound interest? Simple interest pays only on principal, while compound interest folds each period of interest back into the principal. The longer the term and the higher the rate, the wider the gap: in the 20-year example compounding adds 135,782.09, while the same inputs over 40 years produce a gap of 1,190,271.13, 8.77 times larger
- Is a 4% nominal rate the same as 4% effective? No. A 4% nominal rate compounded monthly is 4.0742% effective, because interest earned each month starts earning within the year. When comparing products with different compounding frequencies, convert everything to EAR first, which the frequency table does
- How much do beginning and end-of-period contributions differ? Only the annuity part changes, shifting each contribution one period earlier and multiplying the annuity future value by (1 + periodic rate). At 0.333% monthly over 20 years the difference is 3,667.75, modest at first but larger with longer terms and bigger contributions
- Is the rule of 72 accurate? It estimates doubling time as 72 divided by the annual percentage, and is closest between 6% and 10%. At 15.7% it gives 4.58 years against an exact 4.75, about 61 days short. The error grows at very high or very low rates, and the rule of 69.3 is closer for continuous compounding
- Can CAGR mislead? Yes. It depends only on the first and last values and the number of years, so a portfolio that halves then doubles back to its starting point has a CAGR of 0%, erasing the drawdown. It is a comparison tool across periods, not a risk measure; read it alongside maximum drawdown
- Should inflation be subtracted? Yes. The real return is (1 + nominal) / (1 + inflation) - 1, so 4% nominal with 2% inflation is only 1.96% real. This tool does not account for tax, fees or inflation, which must be deducted separately
- Is the reverse-solved rate reliable? It assumes a constant rate, full and uninterrupted contributions throughout. Real products fluctuate, so treat the result as the average return you must achieve, not as a product quote