Calculating the future value of an account that taxes interest and dividends on an annual basis requires a basic understanding of future value interest factors (FVIFs).
The formula utilized to calculate the FVIF which takes into account this method of taxation is as follows:
The annual taxation on dividends is reflected in the formula above by adjusting the rate of return by the quantity (1 – tax on dividends). The formula for accrual based taxes on interest is identical:
The only difference between the two formulas is the use of subscript “d” versus subscript “i”.
Let’s assume that an investment paid an annualized rate of interest of 4% for ten years, and the annual tax on interest was 15%. Plugging those values into the formula above would yield the following:
If your initial investment was $1,000, you could calculate the future value in the tenth year by multiplying $1,000 by the FVIF of 1.3970:
Using Excel we can construct a FVIF table that takes into account different rates of taxation on interest or dividends, the FVIF table below is constructed with a discount rate of 4%:
| t-interest | |||||
| year | 10% | 15% | 20% | 25% | 30% |
| 1 | 1.03600 | 1.03400 | 1.03200 | 1.03000 | 1.02800 |
| 2 | 1.07330 | 1.06916 | 1.06502 | 1.06090 | 1.05678 |
| 3 | 1.11193 | 1.10551 | 1.09910 | 1.09273 | 1.08637 |
| 4 | 1.15196 | 1.14309 | 1.13428 | 1.12551 | 1.11679 |
| 5 | 1.19344 | 1.18196 | 1.17057 | 1.15927 | 1.14806 |
| 6 | 1.23640 | 1.22215 | 1.20803 | 1.19405 | 1.18021 |
| 7 | 1.28091 | 1.26370 | 1.24669 | 1.22987 | 1.21325 |
| 8 | 1.32702 | 1.30667 | 1.28658 | 1.26677 | 1.24723 |
| 9 | 1.37479 | 1.35109 | 1.32775 | 1.30477 | 1.28215 |
| 10 | 1.42429 | 1.39703 | 1.37024 | 1.34392 | 1.31805 |
Obviously, the higher the rate of taxation the more it will reduce the FVIF.
The Excel model for FVIFs based on annual accrual taxation can be found here.