# Planning for the future

Sometimes, Common Core State Standards aren’t quite high enough.  Being able to write an equation, evaluate it for a given value, and interpret the result is a fundamental academic skill.  Being able to customize equations to model a real-world situation and solve an actual problem makes the academics worthwhile.  One advantage to tiny class sizes is we can move on as soon as students are ready and have consequently covered our pre-calculus material with a week to spare.  It’s time for a project!

In pre-calculus, we have been studying exponential and logarithmic relationships for the last month.  One classic example of exponential growth is interest earning accounts.  If you invest \$4,000 in an account that earns 4.2% interest compounded monthly, how much money is in the account after 8 years?  20 years?  How long does it take for the principal to triple?  Those answers can be found with a fairly simple exponential equation.  But how common is that?  Other than relatives starting a college fund for a newborn, very few accounts involve an initial payment with fixed rates and no deposits or withdrawals for two decades.  Actual finance scenarios are more complex, so we have been using the computational power of spreadsheets to analyze personal debt.

If you have \$2200 of credit card debt with 18% APR and make the minimum payment each month, how long does it take to pay off?  How much interest do you pay?  What is the difference if you add \$10/month to each payment?  If you buy a home for \$220,000 at 5.6% APR, how much of a difference on payments and total interest does a \$50,000 down payment make?  How do your load terms change if you decrease the interest rate by 1.2%?  What about a 30-year mortgage vs. 15 years?  Those are the types of questions Jessica has been tackling through a clever layout of spreadsheets and some research of interest rates.  This is some of her reflection.

“The time difference between the two mortgages makes a huge difference in the amount paid to the bank.  The 30-year mortgage may look better than the 15-year one at first because the buyer pays around \$400 less per month, but overall, the shorter mortgage is ideal, saving nearly \$100,000 in interest.”

“With the down payment, the monthly payments dropped by over \$400 per month, effectively saving the buyer over \$74,000.”

“If you only make the minimum payment each month and still put \$350 on the card at Christmas each year, it puts you in a never ending spiral of debt.”

“Adding just \$10 to the minimum credit card payment makes a phenomenal difference.  Maybe you should skip that latte once in a while.”

Visa is going to hate me for this.  Up next on the agenda, Jessica is researching what banks look for when considering a loan and how an individual can build their credit score.  She is also studying student debt scenarios and getting a grasp on when debt is helpful vs. when it is a curse.  The best part of this project is that it’s both fun and realistic.  We’re using clever problem solving skills and basic programming strategy to construct the spreadsheets, then finding ourselves routinely shocked by the magnitudes of interest payments.

-Dan Thurber, Alzar School Math Teacher