# More Maaser and Tax Math

Let's say your income before taxes and contributions was $1,111, and your tax rate is 10%. Ordinarily, you would pay$111.10 in taxes, and have $999.90 left over, which would be eligible for maaser. So you would need to pay$99.99 in maaser.

But if you paid the $99.99 in maaser, you would then be able to deduct$99.99 from your taxable income, making your taxes only $101.101 (assuming you had stayed in the same bracket). This means you would have$1009.899 to pay maaser on, and would owe $100.9899 in maaser. So, in addition to the possible almost$10 deduction in your net maaser contribution from getting a tax break (as suggested in this question), could there possibly be a further "deduction" in the sense that you now have more income to pay maaser on? And what about after you pay that maaser and get another tax break? How far does it go?

(I'm more interested in whether this is addressed in halacha than whether it is mathematically or practically feasible, since I'm pretty sure it is both of those.)

Is maaser calculated pre-tax or after-tax?

Does Ma'aser count if you have an ulterior motive?

• Sorry I chose bad numbers. Anyone more capable than me is welcome to edit this question to make them cleaner. Thanks in advance :) – SAH Mar 15 '15 at 4:06
• What's wrong with simply running the numbers? That's how we calculate all tax breaks. Consider if you are calculating numbers for a tax deduction that then qualifies for tax - like paying taxes on your QTP to qualify for an education tax credit. Either way, it's a mathematical problem with no relationship to Halacha. – LN6595 Mar 15 '15 at 22:08
• I am thinking that it is similar to the following. Say you pay Federal, State and City tax, as one would in New York City. The percentage of tax you pay is based on Gross Income. For arguement sake, say you pay 25% Federal. Once you pay Federal tax of $12.5K, you really now only have$37.5K left. BUT you still have to pay State and City taxes on the full \$50K. So when paying Maaser, it would be based on Net Income. The amount of Maaser you deduct on your income taxes is based on how much you donated LAST year. What you give in Maaser this year is deducted on next year's taxes. – JJLL Mar 15 '15 at 22:09
• – SAH Mar 6 '18 at 22:15

I don't know whether my answer describes real situation — it is an idealized model. Firstly, you get income. Based on this, let us define:

• base Ma'aser income, , based on which Ma'aser is paid. It means that you should give (where ) to your local Rebe.
• base state tax income, , analogously — tax is payed based on this value. In general, what you should pay is a function , it does not have to be necessarily linear.

Of course,

• and

• (you pay Ma'aser with tax deducted and vice versa).

Therefore, you need to calculate solution to equation .

The analytical solution doesn't have to necessarily exist. You can use any iterative method of root calculation to get the numerical result for , for instance Newton's method. When you finally have it, you pay Ma'aser and of tax. This equation is analytically solvable in special cases. For instance, let us assume that .

It is a linear progression --- if you pay 17% of tax, . In such case .

Solution to this equation for is .

Analogously, .

The answer (how much should you pay) in case of linear progression is thus

• of state tax,

• of Ma'aser, where EDIT: In answer to OP question in comments --- checking the convergence that is --- let us generalize variables to have explicit time dependence. Thus,

• is base income used in calculation of Ma'aser in —th month. The superscript is not a power — it is just an index of sequence,
• is base income used in calculation of state tax in —th month.

So that in one particular ( —th) month one owes Ma'aser and pays of tax (in linear model, I assume constant as well). We can write equations analogous to the previous ones, but now what matters in —th month is how much one paid in previous one:

• and

• .

Reindexing ( and ) the first equation and putting second into first yields .

This iterative equation can be solved the following way: we split into constant and variable part: .

The choice is of course not unique. We want to choose such that equation for has simple form. Combining the two previous equations yields The equation for is really simple when ,

i.e., the constant terms are canceling each other. Then, ,

and since , when . It means that in long time , which is .

This is exactly the answer for calculated in previous section. Therefore, regardless of initial conditions, if one only follows the rules that tax payed in —th month determines amount of Ma'aser in —th month (and vice versa), he/she eventually reaches the proper (`equilibrium') amounts of Ma'aser and tax.

• Actually the OP mentioned "more interested in whether this is addressed in halacha" – Danny Schoemann Mar 15 '15 at 15:41
• As I point out, since you "owe" ma'aser and pay it as a snapshot, you do not need to go through the calculation. Just snapshot net income and pay ma'aser. Paying taxes is also a snapshot and pay taxes owed as of that moment. The next ma'aser snapshot is then based on net income at that later time. – sabbahillel Mar 15 '15 at 17:36
• @DannySchoemann You're right. Nonetheless this is fascinating and involved considerable effort and, since I am an anarchist, I'm going to accept it. – SAH Apr 3 '15 at 3:04

That is one reason that many people calculate the gross ma'aser as after withholding and then count any income tax refund as "income" for the purpose of ma'aser after the tax has been paid. Thus, the recursion that you suggest does not occur. Halachically, the ma'aser owed is calculated at particular times (even if you keep track each month).

If on the other hand you do not have a refund, then you did not have any extra "income".

Since you "owe" ma'aser and pay it as a snapshot, you do not need to go through the calculation. Just snapshot net income and pay ma'aser. Paying taxes is also a snapshot and pay taxes owed as of that moment. The next ma'aser snapshot is then based on net income at that later time.

• I am awarding you a bounty in lieu of an "accept." Nice answer and I only didn't choose it because I am capricious – SAH Apr 3 '15 at 3:05