Rashi on 22;24--
Interest (root word is the same as "snake")- This means increase, for it is like the bite of a snake, for a snake bites a small wound in one's foot and [the victim] does not feel it, but suddenly it causes puffiness and swelling up to the crown of his head. So it is with interest. He does not feel it and is not aware of it, until the interest accumulates and causes him a loss of much money.
Definitions:
Principal: An original sum of money
Interest (or Simple Interest): A calculated percentage value of the principal amount
Compound Interest: A method of calculating interest, where the previous interest is added to the principal amount for future interest calculations
In my experience, interest is a particularly confusing concept for students. I believe that this stems from the somewhat complex aspects of the calculation. In order to calculate interest, you need to first convert the percentage (interest rate) into a decimal or fraction in order to make the calculation. Once you've made the calculation, you have only actually calculated the interest amount. When using interest, the interest is paid on top of the original principal amount. So, in order to calculate the full amount, you need to then add the interest amount together with the original principal amount. The combination of a calculation requiring conversion within a two-step calculation problem, tends to lead to a lot of confusion for many students. Breaking down the steps into a logical progression and making each step meaningful to students can help them make sense of the process, rather than forcing them to memorize a seemingly complex rote process.
Connection to Parsha:
Rashi explains that we are commanded not to charge interest on a loan because the interest builds up without the borrower realizing and suddenly the borrower owes a great amount of money to the lender. Let's use an example to understand Rashi's explanation of how interest accrues and how it can surreptitiously overtake a borrower.
Let's assume that I borrow $1,000 from a friend of mine, and he charges me just 1% interest per week on my loan. Since the parsha doesn't specify simple or compound interest, let's see how they compare side-by-side over the course of 3 months or a 13 week period.
Since we are calculating 1%, we change it into a fraction or decimal (1/100 or .01) in order to calculate with the number (See if you can use the information from Parshat Vayigash to work backwards to create the fractions/decimals for calculation with a percent). Then, we multiply the fraction or decimal times the principal amount. Once we have the weekly interest, we add the interest to the principal to see what is owed each week that the loan goes unpaid. For Simple Interest, we just have $10 interest that adds to the total each week; for Compound Interest, we need to recalculate 1% of each week's new total to calculate the new interest for the following week, and the new interest is added to the previous sum that was owed.
| Simple Interest | Compound Interest | |
| Initial Loan | $1,000 | $1,000 |
| Week 1- interest | $10 | $10 |
| Week 1- total due | $1,010 | $1,010 |
| Week 2- interest | $10 | $10 |
| Week 2- total due | $1,020 | $1,020 |
| Week 3- interest | $10 | $10 |
| Week 3- total due | $1,030 | $1,030 |
| Week 4- interest | $10 | $10 |
| Week 4- total due | $1,040 | $1,041 |
| Week 5- interest | $10 | $10 |
| Week 5- total due | $1,050 | $1,051 |
| Week 6- interest | $10 | $11 |
| Week 6- total due | $1,060 | $1,062 |
| Week 7- interest | $10 | $11 |
| Week 7- total due | $1,070 | $1,072 |
| Week 8- interest | $10 | $11 |
| Week 8- total due | $1,080 | $1,083 |
| Week 9- interest | $10 | $11 |
| Week 9- total due | $1,090 | $1,094 |
| Week 10- interest | $10 | $11 |
| Week 10- total due | $1,100 | $1,105 |
| Week 11- interest | $10 | $11 |
| Week 11- total due | $1,110 | $1,116 |
| Week 12- interest | $10 | $11 |
| Week 12- total due | $1,120 | $1,127 |
| Week 13- interest | $10 | $11 |
| Week 13- total due | $1,130 | $1,138 |
You'll notice in the calculations above that the compound interest doesn't seem much different from the simple interest for almost the full first half of the loan period. This is because we used such a small interest rate.
Let's say that my friend is not as nice to me, and charges me just a little bit more, say 5% interest. Below we'll see a much bigger difference.
| Simple Interest | Compound Interest | |
| Initial Loan | $1,000 | $1,000 |
| Week 1- interest | $50 | $50 |
| Week 1- total due | $1,050 | $1,050 |
| Week 2- interest | $50 | $53 |
| Week 2- total due | $1,100 | $1,103 |
| Week 3- interest | $50 | $55 |
| Week 3- total due | $1,150 | $1,158 |
| Week 4- interest | $50 | $58 |
| Week 4- total due | $1,200 | $1,216 |
| Week 5- interest | $50 | $61 |
| Week 5- total due | $1,250 | $1,276 |
| Week 6- interest | $50 | $64 |
| Week 6- total due | $1,300 | $1,340 |
| Week 7- interest | $50 | $67 |
| Week 7- total due | $1,350 | $1,407 |
| Week 8- interest | $50 | $70 |
| Week 8- total due | $1,400 | $1,477 |
| Week 9- interest | $50 | $74 |
| Week 9- total due | $1,450 | $1,551 |
| Week 10- interest | $50 | $78 |
| Week 10- total due | $1,500 | $1,629 |
| Week 11- interest | $50 | $81 |
| Week 11- total due | $1,550 | $1,710 |
| Week 12- interest | $50 | $86 |
| Week 12- total due | $1,600 | $1,796 |
| Week 13- interest | $50 | $90 |
| Week 13- total due | $1,650 | $1,886 |
From these two examples, we can really see what Rashi is referring to when he talks about interest accumulating quickly without the borrower realizing what he has entered into.
No comments:
Post a Comment