Present Value
Welcome to this page, which features comprehensive Present Value Interest Factor (PVIF) tables. These tables represent a cornerstone tool in the field of financial mathematics, rooted deeply in the fundamental concept of the time value of money. This principle acknowledges that a unit of currency today is worth more than the same unit of currency received in the future, primarily due to its potential earning capacity (interest) or the effects of inflation.
The PVIF itself is often referred to as the discount factor. What it quantifies is the value *today* of receiving exactly one unit of currency – be it $\textsf{₹}1$, $1, or any other denomination – at a specified point in the future, given a certain assumed rate of return or discount rate. In essence, the PVIF tells you how much you would need to invest today, at a particular interest rate, to have one unit of currency at a future date.
The primary application of PVIF tables is to calculate the Present Value (PV) of a *single* future cash flow. If you anticipate receiving a specific amount of money at a future date, these tables allow you to determine its equivalent value in today's terms. This conversion is vital because it enables comparison of cash flows that occur at different points in time on a common basis (present value).
The structure of PVIF tables is designed for ease of use. They are typically organized with rows representing the number of periods (e.g., years, months, quarters) until the future cash flow is received, and columns representing various discount rates (interest rates) per period. To find the appropriate present value factor, you simply navigate the table to the intersection of the relevant number of periods and the applicable discount rate.
Once you have located the correct PVIF from the table, calculating the Present Value of the future cash flow is straightforward: you multiply the future cash amount by this factor. The underlying formula used to generate the values within these tables is: $$ \text{PVIF} = \frac{1}{(1 + r)^n} $$ Where '$r$' represents the discount rate (or interest rate) per period, and '$n$' represents the number of periods until the cash flow occurs. These tables provide pre-calculated values of $\frac{1}{(1 + r)^n}$ for a wide range of 'r' and 'n'.
PVIF tables significantly simplify the process of discounting future cash flows, eliminating the need for repetitive calculations using the formula. They are considered essential resources in various financial contexts, including:
- Investment Appraisal: Evaluating the current worth of future returns from an investment.
- Bond Valuation: Determining the present value of future interest payments and the principal repayment.
- Loan Analysis: Calculating loan payments or the present value of future loan receipts.
- Personal Financial Planning: Assessing the present value of future savings goals or expenses.
By providing these factors, this resource facilitates crucial calculations needed to compare financial opportunities and obligations occurring at different times, making sound financial decisions possible.
This table shows the discount factor for an amount at the end of $n$ period at $r%$
| Periods | Interest Rates (r) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| (n) | 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% |
| 1 | .990 | .980 | .971 | .962 | .952 | .943 | .935 | .926 | .917 | .909 |
| 2 | .980 | .961 | .943 | .925 | .907 | .890 | .873 | .857 | .842 | .826 |
| 3 | .971 | .942 | .915 | .889 | .864 | .840 | .816 | .794 | .772 | .751 |
| 4 | .961 | .924 | .888 | .855 | .823 | .792 | .763 | .735 | .708 | .683 |
| 5 | .951 | .906 | .863 | .822 | .784 | .747 | .713 | .681 | .650 | .621 |
| 6 | .942 | .888 | .837 | .790 | .746 | .705 | .666 | .630 | .596 | .564 |
| 7 | .933 | .871 | .813 | .760 | .711 | .665 | .623 | .583 | .547 | .513 |
| 8 | .923 | .853 | .789 | .731 | .677 | .627 | .582 | .540 | .502 | .467 |
| 9 | .914 | .837 | .766 | .703 | .645 | .592 | .544 | .500 | .460 | .424 |
| 10 | .905 | .820 | .744 | .676 | .614 | .558 | .508 | .463 | .422 | .386 |
| 11 | .896 | .804 | .722 | .650 | .585 | .527 | .475 | .429 | .388 | .350 |
| 12 | .887 | .788 | .701 | .625 | .557 | .497 | .444 | .397 | .356 | .319 |
| 13 | .879 | .773 | .681 | .601 | .530 | .469 | .415 | .368 | .326 | .290 |
| 14 | .870 | .758 | .661 | .577 | .505 | .442 | .388 | .340 | .299 | .263 |
| 15 | .861 | .743 | .642 | .555 | .481 | .417 | .362 | .315 | .275 | .239 |
| 16 | .853 | .728 | .623 | .534 | .458 | .394 | .339 | .292 | .252 | .218 |
| 17 | .844 | .714 | .605 | .513 | .436 | .371 | .317 | .270 | .231 | .198 |
| 18 | .836 | .700 | .587 | .494 | .416 | .350 | .296 | .250 | .212 | .180 |
| 19 | .828 | .686 | .570 | .475 | .396 | .331 | .277 | .232 | .194 | .164 |
| 20 | .820 | .673 | .554 | .456 | .377 | .312 | .258 | .215 | .178 | .149 |
| Periods | Interest Rates (r) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| (n) | 11% | 12% | 13% | 14% | 15% | 16% | 17% | 18% | 19% | 20% |
| 1 | .901 | .893 | .885 | .877 | .870 | .862 | .855 | .847 | .840 | .833 |
| 2 | .812 | 797 | .783 | .769 | .756 | .743 | .731 | .718 | .706 | .694 |
| 3 | .731 | .712 | .693 | .675 | .658 | .641 | .624 | .609 | .593 | .579 |
| 4 | .659 | .636 | .613 | .592 | .572 | .552 | .534 | .516 | .499 | .482 |
| 5 | .593 | .567 | .543 | .519 | .497 | .476 | .456 | .437 | .419 | .402 |
| 6 | .535 | .507 | .480 | .456 | .432 | .410 | .390 | .370 | .352 | .335 |
| 7 | .482 | .452 | .425 | .400 | .376 | .354 | .333 | .314 | .296 | .279 |
| 8 | .434 | .404 | .376 | .351 | .327 | .305 | .285 | .266 | .249 | .233 |
| 9 | .391 | .361 | .333 | .308 | .284 | .263 | .243 | .225 | .209 | .194 |
| 10 | .352 | .322 | .295 | .270 | .247 | .227 | .208 | .191 | .176 | .162 |
| 11 | .317 | .287 | .261 | .237 | .215 | .195 | .178 | .162 | .148 | .135 |
| 12 | .286 | .257 | .231 | .208 | .187 | .168 | .152 | .137 | .124 | .112 |
| 13 | .258 | .229 | .204 | .182 | .163 | .145 | .130 | .116 | .104 | 0.93 |
| 14 | .232 | .205 | .181 | .160 | .141 | .125 | .111 | .099 | .088 | .078 |
| 15 | .209 | .183 | .160 | .140 | .123 | .108 | .095 | .084 | .074 | .065 |
| 16 | .188 | .163 | .141 | .123 | .107 | .093 | .081 | .071 | .062 | .054 |
| 17 | .170 | .146 | .125 | .108 | .093 | .080 | .069 | .060 | .052 | .045 |
| 18 | .153 | .130 | .111 | .095 | .081 | .069 | .059 | .051 | .044 | .038 |
| 19 | .138 | .116 | .098 | .083 | .070 | .060 | .051 | .043 | .037 | .031 |
| 20 | .124 | .104 | .087 | .073 | .061 | .051 | .043 | .037 | .031 | .026 |