## Thursday, September 11, 2008

### Million-Dollar Pennies

A recent article at My Dollar Plan caught my eye: A Penny Saved is ... \$6,977.03! This article points to the essay Every Penny Counts by Scott Bilker.

Bilker shows that if you increase payments on a long-term high interest debt by just a penny each month, big savings result. Starting with a \$10,000 loan at 1.5% per month, the interest is \$150 per month. The minimum you can pay and still have the loan paid off eventually is \$150.01. But this will take about 54 years. Increasing the payment to \$150.02 saves you \$6977.03 over the life of the loan. Just a penny per month makes a big difference.

Now I understand the point these authors are making: small amounts can add up. Ignoring small amounts each day can seriously hurt your finances over the long run. I’ve made the same argument myself in Small Amounts Add Up, but Pennies Don’t. As you can guess from this article’s title, I argue that small amounts add up, but pennies are just too small to amount to anything important.

But, doesn’t Bilker’s example prove the opposite? No, because it is too contrived. It just shows that you should avoid high-interest loans.

Let’s take Bilker’s argument to the next level. Suppose that you have a department-store credit card that charges 2.4% per month. You build it up a \$10,000 balance, and then pay the exact amount of the interest, \$240, each month. Your balance should stay at \$10,000 indefinitely.

But, you didn’t notice a short paragraph in the fine print. There is a one-penny service charge each month. At first your balance goes up by a penny each month, but interest begins to compound over time. After 60 years, you finally notice that something is wrong. How much do you owe at this point? Drum roll, please ... \$10,868,192.14!

Of course, this whole example was silly. Bilker’s example was less silly, but silly nonetheless. It’s about time that we eliminate the penny. The pennies that we hand back and forth in cash transactions can never amount to much. We would be just fine if all cash transactions were rounded to the nearest nickel, or even quarter.

1. Likewise, if the loan payment had been one penny less, he would ultimately have paid an infinite amount of interest! Wow, those pennies really do add up.

Also, if the loan payment had been \$150 plus half a cent, he would also have saved the same \$6980. The savings comes from doubling the rate at which you pay off the principal, not from the pennies themselves.

2. Yeah, that's a strange example the writer gave. If instead of saying the borrower is paying "an extra cent", we say "doubles the payment to principal", the result is more instructive.

The same would be true for someone with an interest-only loan to add a couple dollars to their monthly payment. Wow, suddenly the loan is no longer interest-only. Doesn't make a mortgage that much easier to carry, though.

3. Patrick and Gene:

You make some good observations about doubling the rate of principal payment. However, I don't want to criticize Bilker too much. He is trying to convince people that daily spending on seemingly small things can seriously harm your finances over time, which I strongly agree with. So, I like his "meta" message even if I think pennies are a waste of time.

4. Michael James,

It's just another way of telling the reader that carrying credit card debt is bad. I occasionally read stories about people who have mutual funds and credit card debt. This might make them feel better about their financial situation, but it's a mistake.

There's no mutual funds out there that will return more than 20% every year. Yet, that's what credit card debt often costs.

5. Penny a day is a great example to demonstrate, how pennies can be converted into millions.

I have asked many people this question that if you start with a penny and double it everyday, how much money you will have at the end of 31 days? Nobody answered correctly, and moreover none of them believe that it will add up to a whopping amount of \$10,737,418.24.

Definitely, it is not possible to do it practically, it does however demonstrate the power of penny a day.

Calculations:
1 0.01
2 0.02
3 0.04
4 0.08
5 0.16
6 0.32
7 0.64
8 1.28
9 2.56
10 5.12
11 10.24
12 20.48
13 40.96
14 81.92
15 163.84
16 327.68
17 655.36
18 1,310.72
19 2,621.44
20 5,242.88
21 10,485.76
22 20,971.52
23 41,943.04
24 83,886.08
25 167,772.16
26 335,544.32
27 671,088.64
28 1,342,177.28
29 2,684,354.56
30 5,368,709.12
31 10,737,418.24