Promise to Pay

Posted: October 23, 2026 | Author: David | Filed under: Child Centered Activities, Money & Banking |1 Comment

The November election is hotly contested, overly advertised, and focused upon the wrong issues.  Here in our town, the Public Safety Bond Question asks:

“Shall the city incur indebtedness by the issuance of its general obligation bonds in the principal amount of $88,600,000 for a new fiire (sic) and police station….  Estimated interest cost: $61,798,500 and Total estimated principal & interest: $105,398,500 (sic).”

My son has memorized every piece of equipment for the Department.  He knows which truck number is stationed where, every trucks’ manufacturer, and easily identifies the undercover police cars.  No fool, he knows the Department is spelled “Fire.”  Whoever proofread the ballot should be ashamed of the spelling error.

My son knows that $88.6 + $61.8 is far more than $105 Million.  Therefore, our applied math lesson focused on the amortization of a bond.  His assignment:

“For a new fire and police station, if our town wants to borrow $88.6 Million at 4.5% interest for 30 years, what is the total interest that will be paid?  Over 30 years will the total cost of the station be (a) $120M, (b) $150M, (c) $180M, (d) none of the above?  Show your math.”

With a sharp pencil and paper, we sit down to do math.  Municipal bonds have a vocabulary of their own.  We begin with “Bond Face Amount,” which is the $88.6 Million that the issuer promises to pay over 30 years.  My son wrestles with the concept of amortization, so we begin with the grammar.  We get out the dictionary.

I challenge him, “Is ‘amortize’ a noun or a verb?  What is its grammatical function?”

From his English and Latin, my son knows this drill so he dutifully opens his Thorndike Student Dictionary and turns to A, then to am, then to amo….  He replies, “A transitive verb…extinguish or wipe out (a debt or other liability), usually by setting aside regularly in a special fund certain amounts of money to accumulate at interest.”

I ask, “What is the derivation?”  He studies the page, and then says, “Old French…a form of amortir, which means ‘to deaden, kill, or destroy.’”  He pauses, then says, “Does that mean they are going to kill you if you don’t pay off your debt?”

“No.  You are not killed, but it means the debt is being ‘killed off’.  So our town wants to spend $88.6 Million to build a fire and police station.  They will ‘kill off’ that debt at what total cost?  Our town uses the ‘Equal Annual Principal Amount’ so how much Principal is repaid each year?”  After a long pause he figures that $88.6M divided by 30 equals $2.953 Million.  Per year.  Plus interest.

Our town has a AAA rating by Moody’s and Standard & Poor’s.  I explain how credit ratings work and what is their influence on a bond’s interest rate.

“Can the city pay the bond off sooner than 30 years?” he asks.

I explain, “Imagine you are a money manager in Hong Kong, London, maybe in Boston or over in Portland.  You buy this bond because of its 30-year AAA-rated income stream.  You count on that income.  So you do not want an early payoff option.”

“But if the City pays it off early, won’t it save interest?”

“Most certainly it will,” I answer, “but our city’s 30-year bond is a promise to pay, and that is written into the bond’s terms.  Money managers like certainty.”

“How does the city know it will have the income to pay this?”

My son was getting to the crux of the problem.  I explain, “They will raise taxes.  This bond will mean they have to increase taxes by almost $500 on an average home per year.  They have calculations of all their expenses and all their income, and taxes are how they make up the difference.”

We need to calculate the annual interest.  There is confusion over percentages.  I explain, “100% equals 1.00.  45% equals 0.45.  4.5% equals 0.045.”  I let him use a calculator.  He stares at the paper, not sure whether to calculate against the annual repayment or the face amount.  We go back and forth until he figures out the year 1 interest is $3.987 Million.

I tell him to write the numbers down on the paper, using the standard stacked format, in columns.

Principal repayment = $2,953,333

Year 1 annual interest = $3,987,000

I ask him, “So what is the total payment in year 1?”  He wrestles with this.  There are many numbers on the paper.  I encourage him to stay focused.  I ask, “What are the factors in the total annual payment?”  He needs to do the math.  I lead by asking,  “How much principal is repaid?  And what is the total interest paid in year 1?  Are you going to add, subtract, multiply, or divide?”

“$6,940,333 is the total year 1 payment,” he decides.

“Okay.  Let’s calculate year 2.”  My son works through the entire exercise again.  There are many zeros here, lots of digits.  After a few times going around, he realizes the year 2 outstanding balance is lower than year 1.  Year 2 principal balance is $85,646,667.  He calculates the interest at $3,854,100 and has a eureka moment: “The total payment goes down each year!”

With pencil and paper we do one more year.  His math is accurate.

Uncle Scoop weighs in by text, “Ideally you’ll do the math on the ballot measure twice. Once to calculate the ‘total cost,’ and then again to calculate the real cost. Real vs nominal, important concept. See Fisher equation.”

This is entirely new to me.  Scoop gives us a hint, “Real is less than nominal when inflation is positive.  So if the nominal is 4.5%, real is…”

We do our research.  Irving Fisher was an American economist, statistician, inventor, eugenicist and progressive social reformer.  He has been called by Nobel Prize winning economists “the greatest economist the United States has ever produced.”  His equation expresses that the real interest rate ≈ nominal interest rate − inflation rate.

The ballot measure’s nominal interest rate is 4.5%.  The St. Louis Federal Reserve Bank shows the current 30-year expected breakeven inflation rate is 2.28%.  I do my homework and learn that the exact form of the Fisher equation, (1.045 ÷ 1.0228) − 1, puts the real interest rate at 2.17%.  We need to discount the value of future payments into today’s dollars.  The real interest rate, 2.17%, is what borrowing costs after inflation is factored in, and deflating each payment by the 2.28% inflation rate shows that cost in dollars.

Our conversation turns to the time value of money, and into the dismal science.  Physics is considered a hard science, using mathematics to study fundamental laws of the universe, matter, energy, space and time.  Economics studies human behavior, trade offs, resource allocation, predictions and money.  While physics deals with clear empirical reality, economics deals with scarcity, recessions and inflation; hard truths, and hence it is referred to as the “dismal science.”

But the term originated in the 19th century in a debate about slavery.  The classical economists argued that all humans respond to incentives rather than a racial hierarchy.  Thomas Carlyle, who was pro-slavery, referred to their science as “dismal,” because it supported universal laws rather than the Great Man’s power to lower costs by slavery.

The story of wealth versus human rights is a topic for another class.  My son’s assignment today is to calculate our town’s total cost – the nominal and the real – “to kill off” a debt.  I show how to build an amortization table at the nominal 4.5% rate of interest, and then how to deflate each future payment into today’s Dollars.

Year	Principal outstanding balance	Less principal repayment	Interest annual @ 4.5% = Nominal	Annual Payment	Annual payment adjusted for inflation = Real
1	$‎ 88,600,000	$‎ (2,953,333)	$‎ 3,987,000	$‎ 6,940,333	$‎ 6,785,621
2	$‎ 85,646,667	$‎ (2,953,333)	$‎ 3,854,100	$‎ 6,807,433	$‎ 6,507,317
3	$‎ 82,693,333	$‎ (2,953,333)	$‎ 3,721,200	$‎ 6,674,533	$‎ 6,238,049
4	$‎ 79,740,000	$‎ (2,953,333)	$‎ 3,588,300	$‎ 6,541,633	$‎ 5,977,551
5	$‎ 76,786,667	$‎ (2,953,333)	$‎ 3,455,400	$‎ 6,408,733	$‎ 5,725,568
10	$‎ 62,020,000	$‎ (2,953,333)	$‎ 2,790,900	$‎ 5,744,233	$‎ 4,584,847
20	$‎ 32,486,667	$‎ (2,953,333)	$‎ 1,461,900	$‎ 4,415,233	$‎ 2,812,803
30	$‎ 2,953,333	$‎ (2,953,333)	$‎ 132,900	$‎ 3,086,233	$‎ 1,569,304
	$‎ 0	$‎ (88,600,000)	$‎ 61,798,500	$‎ 150,398,500	$‎ 112,876,907

We can link all of this to the Quadrivium, to Arithmetic, the art of number.  Carl Friedrich Gauss was a German polymath, the “Prince of Mathematicians,” who as a child prodigy is said to have found a summation trick.  Each year’s interest is charged on the balance still owed, which counts down from 30/30 of the loan to 29/30, and on to 1/30.  For any linear progression of numbers, the average is simply the midpoint between the first and last numbers: (1+30)/2=15.5.  The Face Amount of $88.6M times 15.5 = $1,373.3 Million, the sum of all 30 balances.  4.5% of $1,373.3 Million equals $61,798,500 in total interest.  The Gauss shortcut simplifies the entire problem.

Gauss had a shortcut.  We made the table.  Either way, the answers are stunning.  The total interest is $61.8 Million and the nominal cost is $150,398,500.  That is what the ballot should say.  The ballot’s misprint is $105,398,500; the digits are transposed, and no one proofread.  My son has figured out that (b) is the correct answer on his assignment.

The larger lesson, however, is that inflation weakens the United States Dollar over time. The real cost of that 30-year debt, in 2026 Dollars, will be about $112.9 Million.  We teach our children that it is good to save their money, but this lesson teaches that their  savings lose value over time.  $1 today is worth less tomorrow.  It is a paradox: the debt will cost the taxpayers less, while the bondholders are repaid in Dollars worth less than what they lent.  There are two sides to every coin.

The ballot errors led to a lesson on the impact of inflation.  Which means that more than half of his investing gains will be lost just to keep pace with the cost of living.

Dismal, indeed.

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