Tag: interest

Education and the Question of Intuition

An intuition pump is a thought experiment structured to allow the thinker to use his or her intuition to develop an answer to a problem. The phrase was popularized in the 1991 book Consciousness Explained by Tufts philosophy and neuroscience professor, Daniel Dennett.

We argue in this education-completing book, that our intuitions are puzzling in a way that “intuition pump” talk does not cope with at all.

Let’s go immediately to the example of simple versus compound interest in basic finance.

You borrow $100.00 for a year at an annual interest of 100%, without compounding and hence simple. A year passes and you owe the lender the initial $100 plus one hundred percent of this amount (i.e., another hundred). In a year, you owe $200.00, and every year thereafter, if the lender is willing to extend the loan, you owe another hundred to “rent” the initial hundred.

This is written as A+iA, where A is the initial amount (i.e., $100.00) and i is the interest. This can be re-written as A(1+i)n where n is the number of years. Thus, if n=1, you owe: A(1+i), which is 100×2 (i.e., the $200 we just saw). There’s nothing tricky in this.

You then are introduced to compound interest (i.e., where the interest accumulates interest). You can see where compounding by 6 months (semi-annually, or half a year) or 12 months involves dividing the n (the exponent over 1+i) by 12 months, two half-years or 365 days. You could routinely go to days and hours and minutes and seconds and nanoseconds and you could calculate interest payments compounding for each case.

But here is where your intuition falters and fails: suppose you compound continuously?

You get to the number e as growth factor where e=2.71823

Simple algebra does show that at 100% interest, $100 of a loan becomes $100 multiplied by e1 (hundred percent=1) or just e (i.e., you owe $100e).

This gives you $271.82.

So what has happened?

At one hundred percent simple interest you owe $200.00 to the lender. Continuous compounding means you owe $271.82. Instead of owing $100 in interest, you owe $171.82. Your interest bill has gone up by $71.82 or about 72 percent.

Does that seem intuitive? Probably not.

How could one ever apply an “intuition pump” to this arithmetic? We get to the 72% increase in interest by using e which has nothing very intuitive about it. Thus it’s not clear that “intuition pumps” will work here.

You use compound interest arithmetic to get a number which you would never have been able to estimate based on standard intuition since like the 22/7 or 3.14 for π (pi), there’s nothing to “recommend” 2.71823 in and of itself. This means that the link between computational arithmetic understanding and your “gut” or “sixth sense” is feeble at best.

By exploring this way of thinking you could deepen your “meta-intelligence” (i.e., perspective-enhancement). The British economist Pigou (Keynes’s teacher) says that people have a “defective telescopic facility” (i.e., have a poor or even erroneous sense of time-distance).

How one might strengthen one’s sense of time-distance or “far horizons” is not clear.

Third Quarter 2019: Interest Rate Shift Helped Housing but Hurt Bank Net Interest Margins

(from the Federal Reserve Bank of San Francisco)

First Glance 12L provides a first look at banking and economic conditions within the 12th District. The report, “Interest Rate Shift Helped Housing but Hurt Bank Net Interest Margins,” [Archived PDF] notes that District banks’ average quarterly net interest margin slipped as lower interest rates and loan-to-asset ratios weighed on asset yields. The shifting asset mix contributed to margin compression but benefitted average liquidity and risk-based capital ratios. Districtwide loan and job growth cooled but remained above average, and lower interest rates boosted home prices, affordability, and homebuilding. In addition to supervisory hot topics, the report covers wildfire-related risks in California.

Read the full report [Archived PDF].

Essay 95: Education and “Then and Now” Thinking

Ben Shalom Bernanke was Chairman of the Board of Governors of the Federal Reserve System from February 1, 2006, to January 31, 2014.

In many interviews in financial and economic periodicals, he blurts out the fact that his guide in the years surrounding the Great Recession of 2008, in his decisions by the advice of Walter Bagehot of the Economist of London whose main book is called Lombard Street [Project Gutenberg ebook] from 1873:

Lombard Street is known for its analysis of the Bank of England’s response to the Overend-Gurney crisis. Bagehot’s advice (sometimes referred to as “Bagehot’s dictum”) for the lender of last resort during a credit crunch may be summarized by  as follows:

  • Lend freely.
  • At a high rate of interest.
  • On good banking securities.

(Nonetheless, other economists emphasize that many of these ideas were spelled out earlier by Henry Thornton’s book The Paper Credit of Great Britain [archived PDF].)

Bagehot’s dictum has been summarized by as follows: “To avert panic, central banks should lend early and freely (i.e., without limit), to solvent firms, against good collateral, and at ‘high rates’.”

In Bagehot’s own words (Lombard Street [Project Gutenberg ebook], Chapter 7, paragraphs 57–58), lending by the central bank in order to stop a banking panic should follow two rules:

First. That these loans should only be made at a very high rate of interest. This will operate as a heavy fine on unreasonable timidity, and will prevent the greatest number of applications by persons who do not require it. The rate should be raised early in the panic, so that the fine may be paid early; that no one may borrow out of idle precaution without paying well for it; that the Banking reserve may be protected as far as possible.

Secondly. That at this rate these advances should be made on all good banking securities, and as largely as the public ask for them. The reason is plain. The object is to stay alarm, and nothing therefore should be done to cause alarm. But the way to cause alarm is to refuse some one who has good security to offer… No advances indeed need be made by which the Bank will ultimately lose. The amount of bad business in commercial countries is an infinitesimally small fraction of the whole business… The great majority, the majority to be protected, are the ‘sound’ people, the people who have good security to offer. If it is known that the Bank of England is freely advancing on what in ordinary times is reckoned a good security—on what is then commonly pledged and easily convertible—the alarm of the solvent merchants and bankers will be stayed. But if securities, really good and usually convertible, are refused by the Bank, the alarm will not abate, the other loans made will fail in obtaining their end, and the panic will become worse and worse.

We have to ask ourselves: how is it possible that advice from 1873 (i.e., Bagehot’s Lombard Street [Project Gutenberg ebook] crisis-management for that time) can be applicable in 2008?

Does this confirm the off-handed comment in This Time is Different by Ken Rogoff of Harvard that there must be true-but-opaque deep rhythms in history including financial history? Otherwise advice would be useless due to the passage of time and useful patterns would not be discernible.

In fact, Lawrence Summers at Treasury “deluged” Mexico and Latin America with loans to avert an earlier banking crisis following Bagehot’s advice. The logic is that investors must sense that Mexico, etc. will be bailed out at all costs. The idea is to avert a “downward spiral of confidence” by means of visible massive interventions.

Education should always ponder these “then and now” puzzles as part of a beneficial “argument without end.”