Money & Pricing Tables
Time Value of Money: Factor Tables
Every financial calculation on this site is built from four numbers. They are called interest factors, and each one answers a different version of the same question: if money has a price, what is a dollar at one point in time worth at another? Before spreadsheets, these tables were printed in the back of every finance textbook, and analysts read a factor off a page instead of typing a formula.
The four factors are the future value interest factor (FVIF), the present value interest factor (PVIF), and their annuity equivalents FVIFA and PVIFA. They are not four independent ideas — PVIF is the reciprocal of FVIF, and the two annuity factors are the sum of a series of the single-payment factors. Understanding that relationship is what stops the tables from looking like arbitrary numbers.
The tables below run from 1% to 12% and from 1 to 30 years, which covers savings accounts, mortgages, retirement projections and most corporate discounting. Each cell is computed from the closed-form expression, not interpolated, so a value you read here matches what a spreadsheet returns to four decimal places.
Future value interest factor (FVIF): what $1 grows to
| Years | 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% | 12% |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1.0100 | 1.0200 | 1.0300 | 1.0400 | 1.0500 | 1.0600 | 1.0800 | 1.1000 | 1.1200 |
| 2 | 1.0201 | 1.0404 | 1.0609 | 1.0816 | 1.1025 | 1.1236 | 1.1664 | 1.2100 | 1.2544 |
| 3 | 1.0303 | 1.0612 | 1.0927 | 1.1249 | 1.1576 | 1.1910 | 1.2597 | 1.3310 | 1.4049 |
| 5 | 1.0510 | 1.1041 | 1.1593 | 1.2167 | 1.2763 | 1.3382 | 1.4693 | 1.6105 | 1.7623 |
| 7 | 1.0721 | 1.1487 | 1.2299 | 1.3159 | 1.4071 | 1.5036 | 1.7138 | 1.9487 | 2.2107 |
| 10 | 1.1046 | 1.2190 | 1.3439 | 1.4802 | 1.6289 | 1.7908 | 2.1589 | 2.5937 | 3.1058 |
| 15 | 1.1610 | 1.3459 | 1.5580 | 1.8009 | 2.0789 | 2.3966 | 3.1722 | 4.1772 | 5.4736 |
| 20 | 1.2202 | 1.4859 | 1.8061 | 2.1911 | 2.6533 | 3.2071 | 4.6610 | 6.7275 | 9.6463 |
| 25 | 1.2824 | 1.6406 | 2.0938 | 2.6658 | 3.3864 | 4.2919 | 6.8485 | 10.8347 | 17.0001 |
| 30 | 1.3478 | 1.8114 | 2.4273 | 3.2434 | 4.3219 | 5.7435 | 10.0627 | 17.4494 | 29.9599 |
Multiply the amount invested today by the factor for your rate and term. At 8% over 30 years, $1 becomes $10.0627.
Present value interest factor (PVIF): what $1 in the future is worth today
| Years | 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% | 12% |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.9901 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 | 0.9259 | 0.9091 | 0.8929 |
| 2 | 0.9803 | 0.9612 | 0.9426 | 0.9246 | 0.9070 | 0.8900 | 0.8573 | 0.8264 | 0.7972 |
| 3 | 0.9706 | 0.9423 | 0.9151 | 0.8890 | 0.8638 | 0.8396 | 0.7938 | 0.7513 | 0.7118 |
| 5 | 0.9515 | 0.9057 | 0.8626 | 0.8219 | 0.7835 | 0.7473 | 0.6806 | 0.6209 | 0.5674 |
| 7 | 0.9327 | 0.8706 | 0.8131 | 0.7599 | 0.7107 | 0.6651 | 0.5835 | 0.5132 | 0.4523 |
| 10 | 0.9053 | 0.8203 | 0.7441 | 0.6756 | 0.6139 | 0.5584 | 0.4632 | 0.3855 | 0.3220 |
| 15 | 0.8613 | 0.7430 | 0.6419 | 0.5553 | 0.4810 | 0.4173 | 0.3152 | 0.2394 | 0.1827 |
| 20 | 0.8195 | 0.6730 | 0.5537 | 0.4564 | 0.3769 | 0.3118 | 0.2145 | 0.1486 | 0.1037 |
| 25 | 0.7798 | 0.6095 | 0.4776 | 0.3751 | 0.2953 | 0.2330 | 0.1460 | 0.0923 | 0.0588 |
| 30 | 0.7419 | 0.5521 | 0.4120 | 0.3083 | 0.2314 | 0.1741 | 0.0994 | 0.0573 | 0.0334 |
The reciprocal of FVIF. Multiply a future amount by the factor to discount it back to today.
Future value annuity factor (FVIFA): what $1 per year grows to
| Years | 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% | 12% |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 2 | 2.0100 | 2.0200 | 2.0300 | 2.0400 | 2.0500 | 2.0600 | 2.0800 | 2.1000 | 2.1200 |
| 3 | 3.0301 | 3.0604 | 3.0909 | 3.1216 | 3.1525 | 3.1836 | 3.2464 | 3.3100 | 3.3744 |
| 5 | 5.1010 | 5.2040 | 5.3091 | 5.4163 | 5.5256 | 5.6371 | 5.8666 | 6.1051 | 6.3528 |
| 7 | 7.2135 | 7.4343 | 7.6625 | 7.8983 | 8.1420 | 8.3938 | 8.9228 | 9.4872 | 10.0890 |
| 10 | 10.4622 | 10.9497 | 11.4639 | 12.0061 | 12.5779 | 13.1808 | 14.4866 | 15.9374 | 17.5487 |
| 15 | 16.0969 | 17.2934 | 18.5989 | 20.0236 | 21.5786 | 23.2760 | 27.1521 | 31.7725 | 37.2797 |
| 20 | 22.0190 | 24.2974 | 26.8704 | 29.7781 | 33.0660 | 36.7856 | 45.7620 | 57.2750 | 72.0524 |
| 25 | 28.2432 | 32.0303 | 36.4593 | 41.6459 | 47.7271 | 54.8645 | 73.1059 | 98.3471 | 133.3339 |
| 30 | 34.7849 | 40.5681 | 47.5754 | 56.0849 | 66.4388 | 79.0582 | 113.2832 | 164.4940 | 241.3327 |
Assumes the payment lands at the end of each year (an ordinary annuity). For payments at the start, multiply the factor by (1 + i).
Present value annuity factor (PVIFA): what $1 per year is worth today
| Years | 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% | 12% |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.9901 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 | 0.9259 | 0.9091 | 0.8929 |
| 2 | 1.9704 | 1.9416 | 1.9135 | 1.8861 | 1.8594 | 1.8334 | 1.7833 | 1.7355 | 1.6901 |
| 3 | 2.9410 | 2.8839 | 2.8286 | 2.7751 | 2.7232 | 2.6730 | 2.5771 | 2.4869 | 2.4018 |
| 5 | 4.8534 | 4.7135 | 4.5797 | 4.4518 | 4.3295 | 4.2124 | 3.9927 | 3.7908 | 3.6048 |
| 7 | 6.7282 | 6.4720 | 6.2303 | 6.0021 | 5.7864 | 5.5824 | 5.2064 | 4.8684 | 4.5638 |
| 10 | 9.4713 | 8.9826 | 8.5302 | 8.1109 | 7.7217 | 7.3601 | 6.7101 | 6.1446 | 5.6502 |
| 15 | 13.8651 | 12.8493 | 11.9379 | 11.1184 | 10.3797 | 9.7122 | 8.5595 | 7.6061 | 6.8109 |
| 20 | 18.0456 | 16.3514 | 14.8775 | 13.5903 | 12.4622 | 11.4699 | 9.8181 | 8.5136 | 7.4694 |
| 25 | 22.0232 | 19.5235 | 17.4131 | 15.6221 | 14.0939 | 12.7834 | 10.6748 | 9.0770 | 7.8431 |
| 30 | 25.8077 | 22.3965 | 19.6004 | 17.2920 | 15.3725 | 13.7648 | 11.2578 | 9.4269 | 8.0552 |
This is the factor behind every loan payment formula: payment = principal ÷ PVIFA.
How to Use These Tables
- Single amount, moving forward: multiply by FVIF. $5,000 at 6% for 20 years is 5,000 × 3.2071 = $16,035.50.
- Single amount, moving back: multiply by PVIF. $16,035.50 in 20 years at 6% is worth 16,035.50 × 0.3118 = $5,000 today.
- Regular deposits, moving forward: multiply the annual deposit by FVIFA. $200 a year at 5% for 30 years is 200 × 66.4388 = $13,287.77.
- Loan payments: divide the amount borrowed by PVIFA. A $200,000 loan at 5% over 30 years is 200,000 ÷ 15.3725 = $13,010 per year.
- If your rate or term is not in the table, use the formula rather than interpolating between columns — linear interpolation between 7% and 8% is off by up to 0.3% because the factors are exponential, not linear.
Common Questions
What is the difference between FVIF and FVIFA?
FVIF applies to a single lump sum invested once. FVIFA applies to a series of equal payments, one per period. FVIFA is always larger for the same rate and term because it accumulates every payment, not just the first.
Why does PVIF fall as the term gets longer?
Because discounting compounds. At 10%, $1 in 10 years is worth $0.3855 today, and in 30 years only $0.0573. The further away the money is, the less a fixed interest rate leaves of it.
Can I use these factors for monthly payments?
Not directly — the table is annual. For monthly work, divide the annual rate by 12 and multiply the years by 12, then read the same table. A 6% annual rate over 20 years becomes 0.5% over 240 periods, which is outside this table's range, so use the formula.
Do these tables assume payments at the start or end of the period?
End of period, which is the ordinary annuity convention. If payments come at the start — rent, insurance, most subscriptions — multiply the annuity factor by (1 + i) to convert to an annuity due.
What rate should I use?
For savings, the rate you actually earn after tax. For project appraisal, your cost of capital or the return available on a comparable investment. The factor is only as good as the rate, and picking a rate to get the answer you want is the most common way these tables get misused.
More Money & Pricing Tables
Sources
- Compound Interest — Investor.gov — U.S. Securities and Exchange Commission
- Discounting and Present Value — Financial Analysis — U.S. Government Accountability Office, Cost Estimating Guide
- Interest rate risk and the time value of money — Board of Governors of the Federal Reserve System
Filed with Finance calculations.