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It seems that a lot of high school seniors contemplating college are too naive about borrowing and repaying a loan to tell whether a given loan choice is rational or irrational. Or so we are being told.

I would think that the prospect of taking out a major loan, and one from which there is no bankruptcy protection, would be an ideal situation to make a subject like compound interest into a study of real life, practical math.

The goal would be two-fold. First, there's an immediate goal of producing millions of college applicants who are capable of "doing the math" when they are offered a loan and need to decide whether to sign or not to sign.

The second goal is to expose them to some math that goes beyond simple linear proportion problems that they have been dealing with for several years in grade school, and to motivate the lesson with a real-life application.

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    $\begingroup$ Generally banks produce a breakdown for you of the interest and principle paid each year, so you can see how much you are really paying. It may even be legally required to show such information. $\endgroup$ – Steven Gubkin Jun 18 '14 at 12:14
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    $\begingroup$ As for deciding whether to take a loan, there is a simple algorithm which yields good decisions in some 90% cases. It goes like this: "We offer you a loan." "No, thanks." $\endgroup$ – mbork Jun 18 '14 at 20:43
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Instead of a computer simulation, just give them a couple problems that require them to calculate compound interest for different principal amounts and interest rates, then have them plot the results. Use realistic numbers.

Or, give them a more extended problem in which they have an annual income, annual expenses, and a compounded-interest loan. Ask them to figure out how much they can borrow given a certain income, or how much income they need to finance a given loan, or how much they can spend given a loan and their income. Maybe give them a choice between no college, community college, and 4-year college, generate starting post-grad starting salaries that correspond to real data, and have them figure out whether the loans are worth it.

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    $\begingroup$ I think this is a good idea. I think that it can be combined with the idea of using a good spreadsheet program to help with the calculations, and even the plotting. There are pretty good spreadsheets that come with Android these days. So a lot of students already have a spreadsheet in their pocket. $\endgroup$ – Walter Mitty Jun 21 '14 at 12:39
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I would start by making them produce an amortization table for a compound interest loan "by hand" (in a spreadsheet program like Excel). You can have them do a standard amortization table, and then ask the students to look at what happens when (due to some income-based repayment program or other) they are paying less than the computed payment, or worse, less than the total interest due each month, and what happens if they pay an extra $100 per month above what the computed payment for a 10-year amortization is. I think working these examples out manually really drives home how interest works, and how much making reduced payments hurts you, and how much making extra payments saves you.

And yes, then have them compare various scenarios, like whether it is better to take a loan at 6.8% that does accrues interest while they are in college, versus one at 8.0% that does not. (The answer to that depends in part on how many years of college they have left, and how quickly they expect to be able to pay off the loan afterwards.) So that can be a more open-ended question where you ask them to state and justify assumptions, or compare the result for different assumptions, or even figure out where the cutoffs are for when one is better than the other.

(Although I believe federal student loans are actually simple and not compound interest.)

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    $\begingroup$ I have to add though, that even if they totally understand the way interest works, they just don't have the life experience to understand what a $500 payment per month for 10 years is going to feel like. $\endgroup$ – PurpleVermont Jun 18 '14 at 23:56
  • $\begingroup$ That would be a nice addition to the post itself! $\endgroup$ – Mark Fantini Jun 19 '14 at 2:03
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    $\begingroup$ I like the idea of doing things "by hand" in Excel. It gives you a sense of playing with the "what ifs". You could add a little more to the what ifs. What if you end up with the median income for your educational cohort, and end up buying a house with a 20 year mortgage (again, compound interest) at current rates? How much money will you have for discretionary spending? $\endgroup$ – Walter Mitty Jun 19 '14 at 11:48
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    $\begingroup$ @WalterMitty I agree that those types of scenarios are also worthwhile, but much more involved, since it would require figuring out tax rates, do they need a car to get to work and if so car/insurance/gas costs (else transit costs), what will a house cost where they want to live (or apartment), how much will food and heat and light and internet cost, and so on.... All worthwhile but beyond the scope of understanding compound interest. $\endgroup$ – PurpleVermont Jun 19 '14 at 19:42
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    $\begingroup$ Yes, I think that the budget project is one that can be scaled up or down depending on how simple the math has to be, and definitely can be very useful. Maybe "compound interest" could be added to the budget project in later years. $\endgroup$ – Walter Mitty Jun 21 '14 at 2:29
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Combine it with computational modelling / simulation / software!

Most students can't see the connection between sequence or function definitions, proportions and the total money. You need to make it more visual.

  1. Use a simple programming language or high level modelling software to compute iterations of the total value depending on simple models in advertisements/leaflets.
  2. Use plots of functions of different loan cost models / interest models. Let them compare and analyse, under what conditions what model is better.
  3. Create graphical presentations of case overviews: a medical student and an arts student at bank A. The medical student at bank A or bank B.
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