By Bobby Neal Winters
He was in an unpainted shack by the side of the road. Above the entrance was a sign that proclaimed “LOANS.” He sat behind a Dutch door with the top half open. The bottom half was shut and topped with a small shelf that served in lieu of a desk. Setting on it was a piece of wood that proclaimed his name: Mister E.
Mister E dressed in clean but faded overalls. His head was topped with a beat up felt hat. His face was covered with a three-day growth of whiskers and somehow I knew regardless of when I saw him--be it Sunday morning or Saturday night--he would be sporting that three-day growth of whiskers.
Seeing the sign reading loan, I became aware that I had no money, so I decided to borrow some.
“I would like to borrow $100,” I said.
He shook his head back and forth. Then he turned and spat into a spittoon. I must confess I didn’t actually see the spittoon, but I heard something viscous hit brass. He then turned his head back to me and exposed tobacco-stained teeth as he began to speak.
“Nope,” he said. “No, sir. We don’t do it that way. I only loan you a dollar at a time.”
Well, that was strange, but I didn’t have any money at all and borrowing a dollar would allow me to use a pay phone I saw.
Pay phone? When was the last time I saw a pay phone? I must really be out in the boonies.
“Okay,” I said. “May I borrow one dollar?”
“Yes,” he said. “My business is loans, but before you borrow, you must agree to my terms of interest.”
“What is your interest rate?” I asked, a bit concerned. I was out in the backwoods, afterall, where they have their own rules and the law is not always just a phone call away.
He spat again.
“It’s 100 percent per year.”
Ouch, I thought. Well, it’s a good thing he only loans a dollar at a time.
“Okay,” I replied slowly. I wanted to make sure we understood each other. “So if I borrow this dollar, in one year I will pay you back two?”
He smiled through his tobacco-stained teeth and spat again. He could make it ring every time, my God!
“Not so fast,” he said. “We got to compound the interest.”
He began fishing his tongue around in his mouth and gathering up tobacco which he then spat out into his spittoon. It didn’t ring this time, rather there was a dull thud.
He reached into his pocket and pulled out a length of tobacco shaped like a rope.
He laid out the rope of tobacco on the counter in front of him and it was then I noticed there was a calculator and a pad of paper.
“You know how compound interest works don’t you?” he asked. I do, but I could tell he wasn’t really asking. I saw from the look in his eyes and the way his lips parted slightly to expose his ruined teeth that I wasn’t going to be spared a moment of his belabored explanation regardless of what I said. As a consequence of this, I decided to do what I always do in these situations: Play dumb to minimize the pain.
“No,” I lied. “Why don’t you tell me?”
I regretted it the moment I said it because he smiled a hideous smile and then he began.
“Well, when you do simple interest for 100 percent on one dollar, you take the dollar you are loaned, and then to that 100 percent times that and that gives you 1+1=2. But why wait for the whole year to start paying interest? You’ve got my money and I want to have it work for me. Say I only want to wait half a year?”
As if to illustrate his point, he took a pocket knife that had made its way into his hand and cut the rope of tobacco in two.
“When I wait half a year, I can only ask for 50 percent on my money, so I’m owed the borrowed dollar, and then 50 percent of that dollar. That is $1.50 for the first six months. Then after the second six months, I am owed that $1.50 plus the interest on that which is 50 percent of that.”
He put his knife and tobacco down and picked up the pencil to write on the paper:
$1.50+ $1.50 x 0.5
“Now,” he said, “if you do a little al-gee-bree, you can make it pretty.”
He took his pencil and wrote:
$1.50+ $1.50 x 0.50 = 1.50 x 1+ 1.50 x 0.50
= 1.50 x (1+ 0.50)
“That is pretty,” I said in a vain attempt to escape. “Now..”
“You ain’t seen nothing yet,” he said. “Say I want to charge my interest every quarter. Then I cut the hundred percent into four pieces.”
He again took his pocket knife and cut the tobacco rope into four pieces to illustrate. At the end he folded his his knife and put a quarter of the rope into his mouth.
“One quarter of 100 percent is 25 percent. After the first quarter, you owe your dollar plus 25 percent more.”
He wrote it out on his paper:
1+ 1 x 0.25
“Then in the second quarter, you owe that plus 25 percent on it.”
1 + 0.25+ (1 + 0.25) x0.25=(1+ 0.25) x(1+0.25)
“You see,” he said very proud. “You got that square there because you do it for 2 quarters. If you do it for 3 quarters, you’d put a 3, and if you did it for 4 quarters, you’d use a 4. So for a whole year it’s (1.25)4=2.441406.”
He showed the last by using his calculator.
“Now, I think you might see the pattern there,” he said. “If you compounded monthly, you would divide the hundred percent by 12, add that to one, and take the whole thing to the twelfth power. That would be 2.613035.”
His calculator verified this.
“There is a formula for this,” he said. Then he wrote:
“The n is the number of times a year you compound. If you compounded every week, you’d divide the 100 percent by 52, add to one, and raise that to the 52nd power. That would give you 2.692597.”
Again his fingers danced over the calculator, and the number came up as he predicted.
“But if I only compound every week, you are robbing me. If I compound every day, you divide the 100 percent by 365, add that to 1, and raise it to the 365 power. That’s 2.714569.
“But this is my money and every minute it’s gone from my hands it means I can’t loan it to someone else. Now, there are 525,600 minutes in the year.”
I heard the soundtrack of Rent begin to play in the background.
“If I compounded interest every minute, then you would owe me $2.718279 for borrowing that one dollar.”
I was beginning to see that my playing dumb wasn’t going to get me anywhere and that his old dude would compound by the femtosecond if we didn’t cut to the chase, so I cut in.
“Yes, and notice how the numbers are getting closer together: 2, 2.25, 2.441406, 2.613035, 2.692597, 2.714569, and 2.718279. These numbers are all converging toward a number that mathematicians call e. Like pi it is transcendental. Not only does it’s decimal expansion not repeat, but it is not the root of any polynomial with rational coefficients.”
I’d expected the old codger to be annoyed by my cutting him off, but I was wrong. He just smiled.
“Yep, transcendental, that’s me,” he said.
He popped another chaw of tobacco into his mouth and snapped his fingers. With that snap of his fingers everything began to face. The house disappeared first. Then the calculator and pencil.
And then him, with those disgusting teeth absolutely last.
The only thing left was a puddle of tobacco juice where the spittoon had been.