No matter what holiday you celebrate in December, the month has traditionally marked a time for charitable giving.  The weather is growing colder in some areas, making it much tougher on the homeless.  The end of the year is creeping up, and with it the deadline for tax exemptions for charitable giving.  And holiday cheer often means counting our blessings and remembering those who are less fortunate.

Yes, December is the time for giving.  But how much is enough? And what is too much?  As we attempt to balance our own needs (especially in these difficult economic times), many of us struggle with our own sense of guilt and generosity.

We’re at the end of our month of nesting here at Math for Grownups, and I wanted to share a little bit about the math of charitable donations.  Not much makes me feel better about myself than sharing what I have with others. But finding that perfect balance can be a challenge.

Turns out there are formulas that can help guide these decisions.  As we’ve seen in the past, math can remove uncertainty and help us see perspective.  Of course what works for one person is impossible for another.  And that’s okay.  Remember, as grownups we can break the rules — adjust the calculations a bit to suit our personal situations.

Peter Singer, a philosopher who has written about philanthropy, offers an interesting formula.  Singer’s suggestion is based on the amount of income a person or household earns.  His premise is that the larger a person’s income, the more he or she can afford to give.

This is the table adapted from his “The Life You Can Save” website:

INCOMEDONATION
Less than \$105,000At least 1% of your income, getting closer to 5% as your income approaches \$105,000
\$105,001 –\$148,0005%
\$148,001–\$383,0005% of the first \$148,000 and 10% of the remainder
\$383,001 -\$600,0005% of the first \$148,000, 10% of the next \$235,000 and 15% of the remainder
\$600,001 –\$1,900,0005% of the first \$148,000, 10% of the next \$235,000, 15% of the next \$217,000 and 20% of the remainder
\$1,900,001 \$10,700,0005% of the first \$148,000, 10% of the next \$235,000, 15% of the next \$217,000, 20% of the next \$1,300,000 and 25% of the remainder
Over \$10,700,0005% of the first \$148,000, 10% of the next \$235,000, 15% of the next \$217,000, 20% of the next \$1,300,000, 25% of the next \$8,800,000 and 33.33% of the remainder

Most of us are going to fall in the top bracket —  or if you look at your household income, perhaps the second bracket.  And that’s where the math is simple.

Let’s say that Antwan and Jeannette bring in \$75,000 as a couple.  According to Singer, their yearly donations should be between 1% and 5%.  They decide that 2% is a good number for them.

2% of \$75,000

Just in case you’ve forgotten how to do percents, here’s a little refresher.  Two things to know: 1) percents can be written as decimals by moving the decimal point two places to the left.  2) And “of” means multiplication. So that means:

0.02 x 75,000 = 1,500

For Antwan and Jeannette, about \$1,500 is a good annual total for charitable contributions.

But for the wealthy, the math gets a little tougher. Let’s look at another example.

Will earns \$650,000 each year.  According to Singer, he should pay 5% of the first \$148,000, 10% of the next \$235,000, 15% of the next \$217,000 and 20% of the remainder.

One easy way to look at this problem is to first consider four different problems:

5% of \$148,000

10% of \$235,000

15% of \$217,000

20% of the remainder

But what’s the remainder?  Add and subtract to find out:

\$148,000 + \$235,000 + \$217,000 = \$600,000

\$650,000 – \$600,000 = \$50,000

So he’ll need to find 20% of \$50,000.

0.05 x 148,000 = 7,400

0.10 x 235,000 = 23,500

0.15 x 217,000 = 32,550

0.20 x 50,000 = 10,000

Now he just needs to add:

\$7,400 + \$23,500 + \$32,550 + \$10,000 = \$73,450

According to Singer, a good amount for Will to donate over the year is \$73,450.

Of course all charitable giving should be considered in these amounts — from the mittens you donate to the local shelter to the check you send to your United Way.

So do the math yourself — how close are you to Singer’s suggested donation levels?  (If you’re a little too nervous to try, read this first.) Are you surprised to give more?  Do you think you can stretch?  Share your ideas in the comments section.