It is ocassionally helpful for us to refer to the Income Limits set by the U.S. Department of Housing And Urban Development.
These income limit tables are formatted with each income level categories as rows and family size as columns. The following example is from King County, WA 2018:
| Income level | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Very Low | 37450 | 42800 | 48150 | 53500 | 57800 | 62100 | 66350 | 70650 |
| Extremely Low | 22500 | 25700 | 28900 | 32100 | 34700 | 37250 | 39850 | 42400 |
| Low | 56200 | 64200 | 72250 | 80250 | 86700 | 93100 | 99550 | 105950 |
Due to the way some internal systems are set up, we need the tables in a format with each income level cap as a row, and family size as columns. The same example, truncated:
| Income | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 22500 | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low |
| 25700 | Very Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low |
| 28900 | Very Low | Very Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low | Extremely Low |
What's more, a ninth column needs to be added to accomodate families with 9 people.
According to this notice from HUD in 1999 and coroborated in this pdf of methodology for calulating the 2019 limits,
Low-Income Limits: Most four-person low-income limits are the higher of 80 percent of the area median family income or 80 percent of the State nonmetropolitan median family income level. Because the very low-income limits are not always based on 50 percent of median, calculating low-income limits as 80 percent of median would produce anomalies inconsistent with statutory intent (e.g., very low-income limits could be higher than low-income limits). The calculation normally used, therefore, is to set the four-person low-income limit at 1.6 (i.e., 80%/50%) times the relevant four-person very low-income limit. The only exception is that the resulting income limit may not exceed the U.S. median family income level ($47,800 for FY 1999) except when justified by high housing costs. Use of very low-income limits as a starting point for calculating other income limits has the effect of adjusting low-income limits in areas where the very low-income limits have been adjusted because of unusually high or low housing-cost-to-income relationships.
Family Size Adjustments: By statute, family size adjustments are required to provide higher income limits for larger families and lower income limits for smaller families. The factors used are as follows:
Number of Persons in Family and Percentage Adjustments
1 2 3 4 5 6 7 8 70% 80% 90% Base 108% 116% 124% 132%
Income limits for families with more than eight persons are not included in the printed lists because of space limitations. For each person in excess of eight, 8 percent of the four-person base should be added to the eight-person income limit. (For example, the nine-person limit equals 140 percent [132 + 8] of the relevant four-person income limit.) All income limits are rounded to the nearest $50 to reduce administrative burden."