Financial Math class for HS seniors. Input appreciated.

[bigbenreiss]

I posted this in the Anti Mustachian thread and wanted to start a new thread for any input/advice/criticisms.

I teach HS math and have been looking to bring in more and more financial information into the curriculum. Along those lines I have added quite a few projects into other classes on financial planning and budgeting in some classes. I have now gotten the OK from district to create a new "financial modeling with mathematics" class. I needed to name it this way in order to meet the guidelines and requirements for a 4th year class. I will be having the student do quite a bit of projects where they will model different choices.

Keeping in mind that this needs to be math based in order to keep it in the catalog.

What other topics would you include?

Do you have any input for things you wish you learned prior to leaving HS?

I'm trying to make this as comprehensive as possible. I will be writing the units, assessments, projects, Know Understand Do's, and the learning map over the next few months.  Looking for any input from some mustachians so as to make this as useful as possible.

 
Here is the Google.doc link if people would like to give any input.

https://docs.google.com/document/d/1duEUYnocGgFdGUe_SA41oWBpDrSuXfa9sV6Lyi1dkPg/edit?usp=sharing

[Drifterrider]

The best math class I took in HS (I was a sophomore) was math skills everyone uses daily without think about it.

How to add quickly (instructor flipped playing cards and you had to keep a running total.  You didn't have to be exact but you had to be close).  How to quickly calculate a percentage (need a 15% number for a tip.  10% add half again).

How to balance a checkbook.

How to compute compound interest.  How to calculate unit cost (small can of beans or large, which is a better buy)
This was before unit costing was posted on the price tag.

Time value of money.

I have never needed to calculate the volume of a cylinder but I do the above math daily.

[Dee18]

I have snuck some MMM into a class I teach and I think the most important lessons are the chart showing what percent you need to save over how many years to retire and how cutting expenses can be even more helpful then earning more. With a math class both of these concepts would fit right in.  Also showing the students how different a budget is without cable, a car payment eating out, etc and the cost of commuting.  Finally, I would be sure students learned how being frugal in college, thus reducing or avoiding debt, will make life so much easier.  I once saw a poster about how much a latte cost over time when bought with student loan money.  Sounds like a great class!

[pbkmaine]

How to amortize a mortgage and compute PMT, PV and FV. Probabilities. Biases. Sunk cost. IRR. How long it takes money to double. Investing: Ibbotson SBBI chart and correlation coefficients of various asset classes. How to calculate alpha, beta and standard deviation.

[BlueHouse]

My eighth grade history teacher taught us how to fill out a check. No one before or since had ever done that and even though I rarely use checks, I still fill mine out exactly as Mrs. Richards showed.

[KMMK]

In grade 9 advanced math we did tax returns and a fake stock market thing.
All the other consumer math skills are useful. I'd love to teach something like this eventually

[MayDay]

I would focus a lot on student loan math and career choice (aka average salary) math. 

Like if you get an engineering degree, and your student loan is X, what is your monthly budget going to look like.

If you get a teaching degree, and your student loan is Y, what is your monthly budget going to look like. 

If 50% of engineering majors drop out and become philosophy majors, what are the possible trajectories.

etc. 

[laka]

I'd really highlight the way you get more use out of your pre-tax dollars.  As in, you can put that $100 straight into a tax-deferred account (401K, HSA, etc). or you can have them pay you directly and only get $80.  Especially when it's the type of account you may be using soon, say for medical expenses.  Or, looking at it the other way: you can have your paycheck be only $80 lower, but have $100 go directly into your 401K (and then watch it grow).  I feel like the effect choices have on the final paycheck is a pretty big deal for people at this point in their life and understanding what makes that number go up and down and what the benefits are to you is pretty mysterious.  Pointing out the direct connection would help. 

As I think back to my financial education in school, it was really limited to compound interest (but with no context - something to do with saving, but we never really looked at the effects) and writing up a sample budget.  Which was ridiculous, since none of us had any idea how much anything would cost or how much we might get paid.  It would have been great to even be able to look up apartments on craigslist and use that info (no CL way back when). Real world connections - so important.

Also, student loans.  What percentage of your income will you have to spend to pay those back? How does that affect your budget - it's fine to say it'll be a couple hundred a month, but who cares? I'll be making SO MUCH MONEY (compared to current minimum wage job), but really looking at those numbers is different.

[Arktinkerer]

Every student should calculate the cost per hour of college instruction.  Might make them appreciate AP classes and getting the most out of their "free" HS tuition.

[MDM]

How to amortize a mortgage and compute PMT, PV and FV. Probabilities. Biases. Sunk cost. IRR. How long it takes money to double. Investing: Ibbotson SBBI chart and correlation coefficients of various asset classes. How to calculate alpha, beta and standard deviation.

+1

Pretty much covers what I was going to say.  PMT calculation also gets you into the sum of a geometric series.

Other possible topics:
 - choosing lump sum vs. annuity
 - equations behind Excel's NPER (aka "time to FI") calculation
 - the math behind "A invests for a few years then stops but lets the account grow; B waits until A stops, then invests the same amount forever but never catches A"
 - comparing Roth vs. traditional
 - filling out a simple Form 1040

Very interested to see how this works out.  Seems it would be a good addition to the course offerings in our local high schools.  Along that line: does your district use weighted GPAs, and if so what level would this course be?

[BeanCounter]

All the suggestions so far are good. But if I had to pick just ONE topic, it would be compound interest. Both in how it works on the savings/investment side, and how it works when you take out a loan or buy something on credit. Eye opening to see how much regular small investments can grow as well as how much your education, car or house cost in total if you finance it.

[Secretly Saving]

All the suggestions so far are good. But if I had to pick just ONE topic, it would be compound interest. Both in how it works on the savings/investment side, and how it works when you take out a loan or buy something on credit. Eye opening to see how much regular small investments can grow as well as how much your education, car or house cost in total if you finance it.

I second compound interest!

[MyCircus, MyMonkeys]

This is such a great idea, and I wish all high schools considered useful curriculum like this!  I'm taking notes, because I'm going to ask my daughter to do some of these scenarios.  She said yesterday she wanted to tour colleges in New York (we live in Colorado).  She has no idea how much what she's asking costs, and I hope to show her the reality of student loans. 

[BeanCounter]

This is such a great idea, and I wish all high schools considered useful curriculum like this!  I'm taking notes, because I'm going to ask my daughter to do some of these scenarios.  She said yesterday she wanted to tour colleges in New York (we live in Colorado).  She has no idea how much what she's asking costs, and I hope to show her the reality of student loans.

Don't forget to have her calculate what plane flights cost for each and every time she wants to come home. Plus the variance between out of state tuition vs in state. :0

[AlwaysLearningToSave]

If I were doing this, I would start the class by presenting something akin to the following equation: 

Change in Wealth During a Given Period = Earned Income + Unearned Income + Investment Gains - Money Spent - Investment Losses

I would walk the class through this equation to ensure they understand how the different variables relate to one another.  The primary point early on would be to present the idea that if you spend all the money you make, your wealth will not increase unless you are lucky enough that something beyond your control bestowed wealth upon you.  I would also use it as an opportunity to present the concept that if investment gains are high and spending low, wealth increases even if you are not working.  I would start by talking about one month, then one year, ten years, and then a lifetime to emphasize the point that this equation holds true no matter the period of time involved. 

Then throughout the course I would tie every concept and lesson we covered back to this fundamental equation.  Just finished the unit on compound interest?  Go back to this equation and examine how compound interest affects the investment gains variable and the money spent variable.  Where do you want compound interest in your life?

At the end of the course I would work through hypothetical scenarios that involve many of the concepts covered in the class and happen to reinforce frugality and sound financial decisions.  An example might be something like:  Jimmy and Sally each have $35,000 to invest on January 1.  Jimmy invests $35,000 in an asset X.  Sally invests $10,000 in asset Y and $25 in Asset Z.  Asset X losses value at a rate of A.  Asset Y loses value at the rate of B.  Asset Z gains value at the rate of C.  Calculate change in wealth for both Jimmy and Sally after one year and after five years.  Who made the better investments?  Now assume that Jimmy and Sally borrowed money at ___% for 5 years to purchase assets X and Y. 

After everyone has gone through these calculations and discovered that Jimmy was a fool, reveal that you used real data for the problem.  Asset X is a brand new car and the depreciation rate was based on Blue Book Values.  Asset Y was an older used version of (the same / a different) car, also with Blue Book depreciation.  Asset Z was the S & P 500 increasing at its average rate of return during the period. 

[Beaker]

Lot of pretty high-level suggestions here, which is fine. What about just a household budget? You can call it modelling a single family economic unit, if you need to make it sound fancier :)

One of the best things my mom did when I was a kid was sit down and model out a lifestyle. Poke through the classifieds for a job you could get with a high school diploma, find the price of an apartment for rent, find the price of a car, call up for an insurance quote. All that should be easy with the internet, but it forces them to realize that it's all realistic and not some arbitrary numbers.

Then make them take their individual scenarios and project them into the future. Are you going to be rich in 30 years, or broke in 5? Then make them stress test their model life: car problems, health issues, layoffs, etc. Talk about the financial consequences of different solutions to those problems - eg, going into credit card debt vs cutting spending, or using up savings. Maybe also model going to college instead, and figure out when the increased earnings break even with the upfront costs (including debt & opportunity cost).

With a little luck you teach them some good financial skills, make them think realistically about what's waiting for them after graduation, and get them to realize what a trap debt can be.

[AlanStache]

All the suggestions so far are good. But if I had to pick just ONE topic, it would be compound interest. Both in how it works on the savings/investment side, and how it works when you take out a loan or buy something on credit. Eye opening to see how much regular small investments can grow as well as how much your education, car or house cost in total if you finance it.

I second compound interest!

yes but... if you are looking at car loan rates and the cost of interest is 500$ over 4 years I dont think this will impress. 

I guess my first question is how hard do you want to make the math?  Would you want to get into basic programming to have them run different scenarios or just use spreadsheets? 

"One of the best things my mom did when I was a kid was sit down and model out a lifestyle. Poke through the classifieds for a job you could get with a high school diploma, find the price of an apartment for rent, find the price of a car, call up for an insurance quote. All that should be easy with the internet, but it forces them to realize that it's all realistic and not some arbitrary numbers. "
Researching real numbers and applying them is a valuble skill in many different areas

[TheGrimSqueaker]

All the suggestions so far are good. But if I had to pick just ONE topic, it would be compound interest. Both in how it works on the savings/investment side, and how it works when you take out a loan or buy something on credit. Eye opening to see how much regular small investments can grow as well as how much your education, car or house cost in total if you finance it.

I second compound interest!

Isn't compound interest taught in the fifth grade?

[rae]

I taught a grade 12 social science course that looked at families. One of the projects I had them do was plan a wedding.
In groups of two, the 'couple' had to find out what an entry level job would pay in their chosen field; they had to find an apartment to live in and figure out if they would buy, lease, or finance a car, or take public transit; what there monthly expenses would be; what their student debt would be; what their savings rate would be; and so on.
They then had to plan the wedding and either figure out how to pay for it with out blowing all their money, or how many years it would take for them to pay off the wedding.
They really go into the project and phoned around looking for deals on everything from apartments to chair rentals for the event. For many of them, it was an eye-opener for how much life costs. It also showed them what happens when one person has expensive taste and the other does not.

[bigbenreiss]

Just wanted to touch base and say thank you to everyone who gave input. I will be in and out of the thread for a bit. I had surgery this morning and will be working on this during recovery. I just saw the thread with so many idea and suggestions and wanted to take a moment to respond.

The class is going to be CP level, The students taking it are likely not going to be the ones who would have taken Calc instead. The goal will be to put in as much direct research on their parts and having them run different scenarios to model their choices. I like the ideas of showing investing early and often. Pre-tax dollars are something I will definitely be covering.

One issue is mostly in trying to find ways to make these things important to them. The great thing about teenagers is they can have some INSANE optimism about their future career/income. the bad thing about teenagers is its sometimes difficult to get them to look at reality as a back up plan in case they don't become a pro athlete/singer/business owner in the first 5 years after they graduate. 

@rae - I really like that project idea. It could be for any large purchase really.

@MDM -  I think talking about annuity and lump sum is something to look at also. We could have them model a lottery, pension, or insurance payout and the different options.

@beaker -  we will definitely be doing some household budget modeling. The entire idea I have had for this class is to set up students with a basic knowledge and understanding. Have them realize that small sacrifices early (no cable, cheap cell plan, not buying the brand new car) can make huge impacts later. So they have to be modeling their own budgets. 

[dogboyslim]

I'd focus on the cash flows of loans and what a 20k loan really means.

Start with interest across multiple periods. define v=1/1+i.  Then calculate the money needed to invest now to have what you want in the future.  PV = FV*v^t.

Move on to the PV of streams of payments.

n payments of x.  PV = xv+xv^2 + xv^3+...+xv^n

Then teach the sum of a geometric series so you can get to the PV of a stream of equal payments n periods long:
{xv-xv^(n+1)}/{1-v} which simplifies to the PV annuity statement of PV = x*{1-v^n}/i

Once you have this, you can have them calculate the payments amounts of student loans in a given period of time.

With this accomplished, use an example of a credit card, and make them solve the number of years necessary to payoff a credit card balance if paid at the minimum.  You can then also then have them add the total amount paid on a given loan, and show that the longer the loan sits around, the greater the proportion of money repaid goes to interest.

These topics can get you through a good chunk of a semester depending on how many variants you throw at them.  I'd do a loan today where interest accrues and repayments begin in 4 years.  I'd have them think about how much they need to save monthly to hit a desired purchase amount in the future.  Things like that.

The theme of this will help the students understand what they are doing when they take on student loans and credit card debt.  It doesn't help with household budgets, but it is very clearly mathematical in nature.

[randymarsh]

I would definitely do something on student loans. Run repayment repayment calculators, show how the payment effects a monthly budget, etc. Maybe find data that shows spending twice as much money on a "better" school doesn't always translate to vastly better income. Discuss community college and then transferring to a 4 year, if credits transfer.

[Chris22]

I would definitely do something on student loans. Run repayment repayment calculators, show how the payment effects a monthly budget, etc. Maybe find data that shows spending twice as much money on a "better" school doesn't always translate to vastly better income. Discuss community college and then transferring to a 4 year, if credits transfer.

I see the agenda you are pushing, but if the OP shows these things, I hope he/she also shows the financial aid packages available from the same schools.  Plenty of students have found out that wealthy private schools can be more affordable than state schools when financial aid and scholarships are taken into account for students at a certain level. 

[randymarsh]

I would definitely do something on student loans. Run repayment repayment calculators, show how the payment effects a monthly budget, etc. Maybe find data that shows spending twice as much money on a "better" school doesn't always translate to vastly better income. Discuss community college and then transferring to a 4 year, if credits transfer.

I see the agenda you are pushing, but if the OP shows these things, I hope he/she also shows the financial aid packages available from the same schools.  Plenty of students have found out that wealthy private schools can be more affordable than state schools when financial aid and scholarships are taken into account for students at a certain level.

No agenda, I just meant that for the average person there's no point in going to Out Of State U instead of State U unless the out of state one is vastly superior. I agree completely that schools with huge endowments can provide better financial aid packages. I have a friend who's cost for a "public Ivy" ended up being about the same as the cost for my state's cheapest university.

[Chris22]

I also wouldn't assume Out of State U is more than InState U.  Here, Iowa costs a bunch less out of state than Illinois (U-C) in state.  Of course, U of I is a much better school, but still.

[Smokystache]

I've taught a financial literacy course for college students ... easily the most popular class I've ever taught.

One of the biggest problems that I see recent college grad making (and I think this would also apply to HS students), is that they set up their fixed costs to eat up their entire budget (or more). I had my students do some calculations for using X amount of money monthly.

For example, have them run two scenarios where they either A) spend $400 for a car payment (and continually get a new car) or B) Use $150 to save toward a used car (get one every 5 years) and put $250 in a Roth. There are lots of flaws/tweaks in this scenario. But it introduces budgeting, compound interest, debt, tax-advantages accounts, and future value of money in one activity. Have them determine how much net worth Option A or Option B provides at 5, 10, 25, and 40 years. The great thing about working with HS and traditionally aged college students is the time factor of their decisions is huge.

I tell my students something like, "If you have a middle-class income but always have a big car payment, you'll be driving that fancy car to your job when you're 75. Or you can drive your 8 year old Accord to the beach."

[boarder42]

I would definitely do something on student loans. Run repayment repayment calculators, show how the payment effects a monthly budget, etc. Maybe find data that shows spending twice as much money on a "better" school doesn't always translate to vastly better income. Discuss community college and then transferring to a 4 year, if credits transfer.

I see the agenda you are pushing, but if the OP shows these things, I hope he/she also shows the financial aid packages available from the same schools.  Plenty of students have found out that wealthy private schools can be more affordable than state schools when financial aid and scholarships are taken into account for students at a certain level.

I dont think its an agenda.  Its a problem solving game involving math.  "find out what your best path is"  Starts with an inclass work sheet where you draw numbers out of a hat for your scholarships to different schools, you then analyze the best path for you based purely on the math.  Then you could have them do a real world application study.  Many universities offer scholarships pretty standard based on GPA and ACT scrores.  and they could run a cost comparison based on the degrees they are considering pursuing and what the real world starting salaries are to determine the ROI

[nazar]

I would make sure that in the context of explaining compound interest earned from investing that examples of how compounding will grow debt to unmanageable levels, especially if only minimum payments are made.  That should include the effect of different interest rates on debt.  Compound interest can work for you or against you.  This is where things go right or wrong.  Will they be net savers, spenders, or debtors?