In mathematics, there’s a concept known as a step-wise function. Its namesake is owed to what the function looks like when you graph it, it looks like steps or stairs (this is sort of what it looks like).

As you slide across the X-axis, the Y doesn’t jump up until after a certain amount. It’s at those boundaries, where the tiers shift up (or down), that you need to pay the most attention. Why is this little trip down memory lane important? Many things in personal finance are step-wise functions and it’s important to understand them because it can save you a lot of money.

When I discussed the impact of your credit score on your loan interest rates ^{[3]}, I listed a table of scores and rates. If you remember the chart, everyone with a credit score between 760 and 850 would paid an interest rate of 5.766% on a 30 year fixed loan. Someone with a credit score of 759, just a sniff away from 760, would have to pay 5.988% – or 0.222%. One hard inquiry can shift you from one category to another and cost you a few thousand dollars. That one inquiry can take you from step to another and cost you thousands of dollars.

What other personal finance “functions” are tiers?

**IRA contributions (this explanation is for the Roth):**Your contribution limit is affected by your adjusted gross income but it’s not perfectly linear. The range for a single filer for 2008 is $101,000 to $116,000. You figure out how far through the limit you are, then you calculate how much you can contribute but you always round up your contribution limit to the nearest $10. Also, if you calculate your limit to be under $200, you can round up to $200. This means if you can get your AGI from 116,001 to 115,999 – you go from being ineligible to contribute to a Roth IRA to being able to contribute $200. Here’s more information about Roth IRA contribution limits^{[4]}.**Eligibility for Medical Expense Deductions:**You’re able to deduct your medial expenses on your tax return if they are more than 7.5% of your adjusted gross income. It’s one of those ON-OFF situations where if it’s above 7.5% you’re eligible, if it’s under, you’re not. The nice thing about this tier is that there are two sides you can play with, either increase your medical expenses by paying for or purchasing things early or lower your AGI. (**Update:**I made an error in the original, it turns out you can only deduct the medical expenses that exceed the 7.5%, Thanks Fred^{[5]}!)**Income tax underpayment penalty:**This doesn’t happen often but if you have any large capital gains, usually from the sale of stock or your home, you need to be aware of the underpayment penalty rules regarding “safe harbor.” Safe harbor means that if you follow the safe harbor rules, you won’t be subject to underpayment penalties. How do you follow them? First, if you received a refund last year then you are safe this year. If you didn’t, then you have to be sure that you pay either at least 100% of your tax owed last year or pay within 90% of what you owe this year. If you fail to do that, then you will be penalized on the underpayment. If you follow those rules, you are safe. (states have similar rules too but they may be different, in Maryland the safe harbor rule requires payment of 110% of last year’s tax owed, which is 10% more than the federal rule)

Here’s a more comprehensive list of tax phaseouts ^{[6]} if you want to dig a little further into those.

If you can think of anymore of these types of “money tiers,” please let me know in the comments.