The concept of future value and present value interest factors is an important one to understand when you begin to calculate future and present values which take into account more complex forms of taxation.
For instance, to determine the future value of an account that taxes interest or dividends on an annual basis at some specified rate would require you to calculate the future value interest factor using a formula that solves for such method of taxation.
Before the age of calculators and computers, solving future value and present value equations required the use of interest factor tables. Fortunately, solving for the factors is easier than in sounds.
The future value interest factor (FVIF) is simply the quantity that the present value is compounded by:
Let’s construct a future value interest factor table using an assumed annual rate of 7%:
| Rate | ||||||
| 2.00% | 3.00% | 4.00% | 5.00% | 6.00% | 7.00% | |
| Year | ||||||
| 1 | 1.0200 | 1.0300 | 1.0400 | 1.0500 | 1.0600 | 1.0700 |
| 2 | 1.0404 | 1.0609 | 1.0816 | 1.1025 | 1.1236 | 1.1449 |
| 3 | 1.0612 | 1.0927 | 1.1249 | 1.1576 | 1.1910 | 1.2250 |
| 4 | 1.0824 | 1.1255 | 1.1699 | 1.2155 | 1.2625 | 1.3108 |
| 5 | 1.1041 | 1.1593 | 1.2167 | 1.2763 | 1.3382 | 1.4026 |
| 6 | 1.1262 | 1.1941 | 1.2653 | 1.3401 | 1.4185 | 1.5007 |
| 7 | 1.1487 | 1.2299 | 1.3159 | 1.4071 | 1.5036 | 1.6058 |
| 8 | 1.1717 | 1.2668 | 1.3686 | 1.4775 | 1.5938 | 1.7182 |
| 9 | 1.1951 | 1.3048 | 1.4233 | 1.5513 | 1.6895 | 1.8385 |
| 10 | 1.2190 | 1.3439 | 1.4802 | 1.6289 | 1.7908 | 1.9672 |
Let’s assume you wanted to calculate the future value interest factor for an investment that will grow at 7% for ten years, plugging those values into the future value interest factor equation will yield the following:
Using the table above and finding the area where n = 10 and r = 7% intersect indicates that the FVIF is 1.9672. Any dollar amount multiplied by the FVIF of 1.9672 will yield the future value of an investment that grew at 7% for ten years.
Present value interest factors (PVIF) are simply the inverse of FVIFs:
We can construct a PVIF table in the same manner:
| Rate | ||||||
| 2% | 3% | 4% | 5% | 6% | 7% | |
| Year | ||||||
| 1 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 | 0.9346 |
| 2 | 0.9612 | 0.9426 | 0.9246 | 0.9070 | 0.8900 | 0.8734 |
| 3 | 0.9423 | 0.9151 | 0.8890 | 0.8638 | 0.8396 | 0.8163 |
| 4 | 0.9238 | 0.8885 | 0.8548 | 0.8227 | 0.7921 | 0.7629 |
| 5 | 0.9057 | 0.8626 | 0.8219 | 0.7835 | 0.7473 | 0.7130 |
| 6 | 0.8880 | 0.8375 | 0.7903 | 0.7462 | 0.7050 | 0.6663 |
| 7 | 0.8706 | 0.8131 | 0.7599 | 0.7107 | 0.6651 | 0.6227 |
| 8 | 0.8535 | 0.7894 | 0.7307 | 0.6768 | 0.6274 | 0.5820 |
| 9 | 0.8368 | 0.7664 | 0.7026 | 0.6446 | 0.5919 | 0.5439 |
| 10 | 0.8203 | 0.7441 | 0.6756 | 0.6139 | 0.5584 | 0.5083 |
Notice, if you multiply any FVIF by its corresponding PVIF the product of the two numbers will equal one:
Using an HP12C calculator, we can solve for the FVIF in the example above using the following keystrokes:
[1][.][0][7][ENTER]
[10][y^x]
The Excel model for FVIF and PVIF table construction can be found here.