Compound Interest Table – Growth Factors by Rate & Year
Look up future value factors for a lump sum, end-of-year contribution factors, the growth of 1,000 and exact doubling times under annual compounding.
Future value factor table for one lump sum
Choose the row for the number of years and the column for the effective annual rate. Multiply the starting amount by the factor at their intersection.
| Years | 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 10% |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1.0100 | 1.0200 | 1.0300 | 1.0400 | 1.0500 | 1.0600 | 1.0700 | 1.0800 | 1.1000 |
| 2 | 1.0201 | 1.0404 | 1.0609 | 1.0816 | 1.1025 | 1.1236 | 1.1449 | 1.1664 | 1.2100 |
| 3 | 1.0303 | 1.0612 | 1.0927 | 1.1249 | 1.1576 | 1.1910 | 1.2250 | 1.2597 | 1.3310 |
| 5 | 1.0510 | 1.1041 | 1.1593 | 1.2167 | 1.2763 | 1.3382 | 1.4026 | 1.4693 | 1.6105 |
| 10 | 1.1046 | 1.2190 | 1.3439 | 1.4802 | 1.6289 | 1.7908 | 1.9672 | 2.1589 | 2.5937 |
| 15 | 1.1610 | 1.3459 | 1.5580 | 1.8009 | 2.0789 | 2.3966 | 2.7590 | 3.1722 | 4.1772 |
| 20 | 1.2202 | 1.4859 | 1.8061 | 2.1911 | 2.6533 | 3.2071 | 3.8697 | 4.6610 | 6.7275 |
| 25 | 1.2824 | 1.6406 | 2.0938 | 2.6658 | 3.3864 | 4.2919 | 5.4274 | 6.8485 | 10.8347 |
| 30 | 1.3478 | 1.8114 | 2.4273 | 3.2434 | 4.3219 | 5.7435 | 7.6123 | 10.0627 | 17.4494 |
| 40 | 1.4889 | 2.2080 | 3.2620 | 4.8010 | 7.0400 | 10.2857 | 14.9745 | 21.7245 | 45.2593 |
Example: the 20-year factor at 5% is 2.6533. A starting amount of 4,000 therefore grows to approximately 4,000 × 2.6533 = 10,613.20 before costs and tax.
Need a rate, term or contribution not shown here?
The reference values use annual compounding. Open the calculator for exact months, nominal or effective rates and monthly, quarterly or annual contributions.
What 1,000 grows to at selected rates
This table converts the factors into money values. The currency does not affect the mathematics: the same numbers apply to $1,000, €1,000, £1,000 or 1,000 units of another currency.
| Years | 3% | 5% | 7% | 10% |
|---|---|---|---|---|
| 5 | 1,159.27 | 1,276.28 | 1,402.55 | 1,610.51 |
| 10 | 1,343.92 | 1,628.89 | 1,967.15 | 2,593.74 |
| 20 | 1,806.11 | 2,653.30 | 3,869.68 | 6,727.50 |
| 30 | 2,427.26 | 4,321.94 | 7,612.26 | 17,449.40 |
| 40 | 3,262.04 | 7,039.99 | 14,974.46 | 45,259.26 |
The large long-term gaps do not mean a higher return is guaranteed. They show the mathematical consequence of holding a constant rate assumption for many years.
Future value factor for equal end-of-year contributions
The ordinary-annuity factor answers a different question: what is the future value of a fixed contribution made at the end of every year? Multiply the annual contribution by the table factor. No starting lump sum is included.
| Years / payments | 2% | 4% | 5% | 6% | 8% | 10% |
|---|---|---|---|---|---|---|
| 5 | 5.2040 | 5.4163 | 5.5256 | 5.6371 | 5.8666 | 6.1051 |
| 10 | 10.9497 | 12.0061 | 12.5779 | 13.1808 | 14.4866 | 15.9374 |
| 15 | 17.2934 | 20.0236 | 21.5786 | 23.2760 | 27.1521 | 31.7725 |
| 20 | 24.2974 | 29.7781 | 33.0660 | 36.7856 | 45.7620 | 57.2750 |
| 25 | 32.0303 | 41.6459 | 47.7271 | 54.8645 | 73.1059 | 98.3471 |
| 30 | 40.5681 | 56.0849 | 66.4388 | 79.0582 | 113.2832 | 164.4940 |
Example: 2,400 contributed at each year-end for 20 years at 5% gives 2,400 × 33.0660 ≈ 79,358.40. The raw contributions total 48,000; the difference is modelled interest.
For beginning-of-year contributions, multiply the ordinary-annuity result by (1 + annual rate). Monthly contributions require monthly periods and an appropriate monthly rate, so they should not be read directly from this annual table.
Exact doubling time and the Rule of 72
The exact time solves (1 + rate)years = 2. The Rule of 72 is a mental estimate obtained by dividing 72 by the percentage rate.
| Annual rate | Exact doubling time | Rule of 72 estimate |
|---|---|---|
| 1% | 69.66 years | 72.00 years |
| 2% | 35.00 years | 36.00 years |
| 3% | 23.45 years | 24.00 years |
| 4% | 17.67 years | 18.00 years |
| 5% | 14.21 years | 14.40 years |
| 6% | 11.90 years | 12.00 years |
| 7% | 10.24 years | 10.29 years |
| 8% | 9.01 years | 9.00 years |
| 10% | 7.27 years | 7.20 years |
| 12% | 6.12 years | 6.00 years |
The rule is useful for quick orientation, not a replacement for the exact formula. It also assumes that the rate remains constant and gains stay invested.
How to read a compound interest factor
A factor is a multiplier, not a percentage. A factor of 1.6289 means the ending amount is approximately 162.89% of the starting amount. The cumulative gain is therefore 62.89%, not 162.89%.
Because each year’s interest stays in the balance, the path is exponential. Adding the annual rate repeatedly would describe simple interest and would produce a different result. At 5% for 20 years, simple interest gives a factor of 2.0000, while annual compounding gives 2.6533.
Values in the table are rounded to four decimal places. Use an unrounded formula or the calculator when cents matter.
Annual compounding versus nominal rates
The main table treats every column as an effective annual rate with one annual growth step. A nominal quote compounded monthly is different. For example, 6% nominal compounded monthly creates an effective annual factor of (1 + 0.06 ÷ 12)12, approximately 1.061678, rather than exactly 1.060000.
If a product publishes APY or AER, that figure is normally the effective annual rate intended for an annual factor comparison. If it publishes a nominal rate and a separate posting frequency, convert it first. Mixing the two conventions is a common reason a manual table check does not match an account illustration.
Actual providers can also use day counts, changing rates, cash-flow dates and rounding rules not represented in this reference.
Nominal balance is not purchasing power
The tables show nominal mathematical growth. They do not answer how much the future balance can buy. A rough real growth comparison must combine return and inflation multiplicatively:
For example, 5% nominal growth with 2.5% inflation corresponds to about 2.44% real growth before tax and fees, not 2.5% obtained by simple subtraction. Over long horizons, even a small difference between nominal and real rates materially changes the factor.
Keep nominal amounts with nominal rates and inflation-adjusted amounts with real rates. The Inflation Calculator can show the purchasing-power side separately.
For students: choose the correct factor before multiplying
Financial mathematics tables usually separate four factor families: future value of one amount, future value of an annuity, present value of one amount and present value of an annuity. The direction and the number of cash flows determine which table is valid.
- Draw time 0 and the future dates.
- Decide whether there is one amount or a level series.
- Check whether the question moves money forward or backward.
- Match the rate period to the cash-flow period.
- Only then read the factor and multiply.
Exercise: one lump sum
Exercise: annual contribution stream
Limitations of a static compound interest table
- Only selected whole-year terms and rates are shown.
- The rate is constant and positive throughout the entire period.
- The lump-sum table assumes no deposits or withdrawals.
- The annuity table assumes equal end-of-year contributions.
- Fees, taxes, inflation and investment losses are excluded.
- Four-decimal factors create small rounding differences.
Use the table for quick checks, teaching and approximate comparisons. Use a calculator or dated cash-flow model for exact personal schedules.