A Savings Account at the Paleo National Bank

Thanks to my town's Open Meeting Law, I'm able to follow local officials' actions pretty closely. Our Treasurer recently reported that, a few months ago, she switched the town's savings account to the Paleo National Bank. She was attracted by its generous offer of a 6% annual percentage rate. The latest Treasurer's Report included a summary of last month's savings account statement from the PNB. It looked like this:

Beginning-of-month balance: $2,500.00
Deposits: $200.00
Withdrawals: $250.00
Average Daily Balance: $1,841.54
Interest: $6.20
End-of-month balance: $2,443.80.

At first, this looked okay -- but on closer inspection, the arithmetic seemed questionable:

$2,500.00 + $200.00 - $250.00 + $6.20 = $2,456.20

There's a difference of $12.40. It seems that Interest of $6.20 had been debited from rather than credited to the balance:

$2,500.00 + $200.00 - $250.00 - $6.20 = $2,443.80

And wait: the statement says the 6% Interest was calculated on an Average Daily Balance of $1,841.54 -- But the balance couldn't have dropped below $2,250.00, during the month.

If the ADB had actually been about $2,400, the month's interest would have been about $12.00:

$2,400 * 6%/yr * (1 year/12 months) = $12

So the correct End-of-Month Balance should have been about:

$2,500.00 + $200.00 - $250.00 + $12.00 = $2,462.00

The End-of-Month Balance as calculated by the PNB seems to be about $18 too low.

I asked the town's Treasurer about this, but she shrugged. Busy woman; she authorized me to talk to the bank if I wanted. When I phoned, the PNB representative didn't dispute my arithmetic... but he said that the bank had correctly calculated the balance. He repeated this point a number of times.

So I drove to the local branch and met with Ekim, the manager. He reiterated that the PNB's calculations are most certainly correct. He went on to tell me that any claim to the contrary would be bizarre.

I wasn't satisfied by these responses to my queries, so I wrote a Letter to the Editor, and sent it off to our local paper. Over the next few weeks, many senior employees of other banks wrote letters of their own. To my surprise, their accounts all supported Ekim's version, emphasizing that banks such as PNB had skillful senior executives, used rigorous accounting practices, and calculated their customers' balances with sophisticated computers. Many noted that Ekim had just won a "Top Manager" award. In a twist, a few executives darkly recalled the years of bad blood between retail bankers and stockbrokers, intimating that the reason I was raising this issue had to do with unspecified, hidden connections that I must have to the Stockbrokers' Association.

But -- puzzlingly -- none of these bankers would go on the record to explicitly state,

"The correct Interest was $6.20, and it was proper to debit Interest from the town account's balance."

Instead, their contention on how the month's Interest should have been handled boiled down to,

"I don't know, and it doesn't matter."

The arithmetic underlying this controversy is straightforward and thus uninteresting. And the apparent $18 error is indeed rather small, and may not matter, as such.

And yet: Ekim and his supporters in the banking industry have taken a position that seems tough to defend. They are justifying the PNB's handling of the town's account, but without offering any answers to the specific points that have been raised.

What are we to think about how the PNB and similar banks go about their other business?

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Remarks

This post proposes the analogy of a simple and commonplace math problem -- calculating interest due on a savings account -- for the more esoteric dispute about the use of the Tiljander proxies in Mann08 (references, 2009 discussion at Stoat, 'Jarvykortta River' walk-through of one Tiljander proxy, RealClimate.org's Gavin Schmidt defends Mann08 on this topic).

As with every metaphor, this one has weaknesses. Foremost, the tasks undertaken by scientists are ill-defined, challenging, and ever-changing -- in contrast to the focused, routine, and constant aspects of many of a branch manager's responsibilities. Professor Mann and his co-authors had to keep many balls in the air as they readied their 2008 PNAS paper for publication. It's not reasonable to expect perfection.

But I think it is reasonable to expect the prompt acknowledgment and correction of clear-cut errors, once they are identified.

In the story, there's a right way and a wrong to calculate 6% interest -- just as there are right and wrong ways to calibrate paleotemperature proxies to the instrumental temperature record. In both cases, the sign makes a difference, as well. Who ever heard of subtracting earned interest from a savings balance? In similar fashion: how could a proxy signal that communicates "warmer" be transformed into one that signifies "cooler," without an explanation?

One could argue that the PNB's ~$18 error "doesn't matter." After all, it's only 0.7% of the town's final balance. On the other hand, customers assume that (1) the bank's procedures are correct, (2) the bank will follow those procedures, and (3) when mistakes are brought to its attention, they will be corrected. The PNB's attempt to close off discussion effectively disavows this approach.

The support of other banks' employees might be heartwarming to branch manager Ekim, but most outsiders will understand that it is a discredit to the industry, and a public-relations blunder. If colleagues had persuaded Ekim to act according to the proper accounting standards, the issue would have been resolved with only minor embarrassment. By supporting his application of faulty arithmetic, they've encouraged him to "tough it out." Further, the bank executives' campaign will give the public the impression that faulty arithmetic is widely condoned within the banking industry. Unsupported allusions to the malign influence of anti-bank stockbrokers will further erode the reputation of the banking sector. Even if we stipulate that a cabal of brokers and their allies have engaged in much disreputable conduct over the years: that's not the issue here.

The application of arithmetic, logic, common sense, and widely-accepted procedures to a fairly straightforward problem: that's the issue.