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Recently I undertook writing a lesson plan as part of a continuing education exercise. Since the content area is financial literacy, I endeavored to write / plan a lesson RE: earning interest. A simple enough topic, but I soon discovered a significant skeleton in my closet that needed to be exorcised.
One of the things I enjoy about mathematics is the unflinching reliability of the results that can be attained. A simple misstep usually reveals itself unless one fails to use a check on one's work. The "Simple Interest Formula" that I came across during my preparation seemed simple enough: I = PRT; where I = the amount of interest earned, P = the principle (or amount of money concerned), R = the rate of interest being paid, and T = the duration of time involved. Here's where I went terribly wrong:
Somewhere in my background I had invented a process of calculating interest by multiplying a principle times 100% of the principal plus the interest rate. For example, if I were asked to calculate the total amount to be paid back in one year for a $100 loan at 5% interest, I would simply multiply $100 x 1.05 x 1 yr. = $105. Easy, right? Easy, correct and seemingly an incorruptible process. But learning the correct application of the Simple Interest Formula shed light on my bad habit.
In order to correctly apply an interest rate in this situation, the rate needs to be expressed in its real terms; meaning its numerical quantity with respect to 100. In other words, 5 percent literally means "per 100"; 5/100 as a fraction or 0.05 if expressed in decimal form. As I've already discussed, the problems don't show up unless one starts to increase the time horizon in a situation. Say I tried to solve the problem my old way if the repayment period were increased. In that case, my old self would have approached the problem like this:
James borrows $100 at 5% interest for 2 years. How much will he ultimately have to pay back?
Using what I thought was the correct application of the Simple Interest Formula, I would have calculated $100 x 1.05 x 2 yrs. = $210. In dollar amounts, maybe not so noticeable, but if one looks at the fact that your erroneous method literally doubles the amount of money to be re-paid. The relatively low interest rate's impact is nothing compared to the payback period. If this same method were used and James had 3 yrs. to pay it all back, we'd literally calculating an amount that was 3 times the original principal.
The solution is to strictly adhere to expressing interest as X parts per 100, X percent or 0.0X. And that is what I "un-learned" today.
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