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# NCTM 2012 Presentation 1

## on Apr 29, 2012

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This is the first of the presentations we gave at the TI booth at NCTM 2012 in Philly.

This is the first of the presentations we gave at the TI booth at NCTM 2012 in Philly.

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## NCTM 2012 Presentation 1Presentation Transcript

• Algebra Resources for the TN-NspireMedia4Math includes a variety of free andpremium resources, including short videotutorials on the Nspire, Math in the News, andother tutorials.
• Algebra Resources for the TN-NspireIn this presentation we will focus on our DVDLibrary, Algebra Applications.
• Algebra Resources for the TN-NspireVolume 1 Volume 21. Linear Functions 6. Functions and2. Quadratic Functions Relations3. Variables and 7. Exponential Functions Equations 8. Logarithmic Functions4. Inequalities 9. Rational Functions5. Data Analysis 10. Systems of Equations
• Algebra Resources for the TN-NspireAlgebra Applications: Data Analysis focuses onthe housing crisis of 2008.
• Algebra Resources for the TN-NspireThe impact of the housing crisis was a steep dropin the stock market.
• Algebra Resources for the TN-NspireThe value of houses on the market began to godown and some had trouble keeping up withsuddenly higher mortgage payments.
• Algebra Resources for the TN-NspireAs a result, the number of foreclosures began toincrease dramatically.
• Algebra Resources for the TN-NspireTo get a better understanding of the housingcrisis, we start with what a mortgage is.
• Algebra Resources for the TN-NspireWe use the TI-Nspire to explore differentmortgage scenarios and also construct anamortization table.
• Algebra Resources for the TN-NspireWe start by opening a Spreadsheet window andlabeling three cells for the loan amount, theinterest rate, and the total number of payments.
• Algebra Resources for the TN-NspireWe input the values shown, and we use theNspire’s Time Value of Money function tocalculate the mortgage amount.
• Algebra Resources for the TN-NspireThe TVMPMT function takes six values: thenumber of payments, interest, loan amount,future value, and payments and compoundingsper year.
• Algebra Resources for the TN-Nspire The future value is set to zero since we’re calculating full repayment of the loan.
• Algebra Resources for the TN-Nspire The result is the monthly mortgage payment, set as a negative value.
• Algebra Resources for the TN-Nspire We can now calculate the full value of the loan, principal plus all interest payments.
• Algebra Resources for the TN-Nspire So, for this mortgage the loan repayment is nearly twice the value of the original loan amount.
• Algebra Resources for the TN-Nspire Why is the repayment so much more than the original loan amount? Each payment is used to pay interest and pincipal.
• Algebra Resources for the TN-Nspire So, let’s add a new column to the spreadsheet to track how the balance on the loan changes with each payment.
• Algebra Resources for the TN-Nspire The Current Loan Balance is made up of these three values.
• Algebra Resources for the TN-Nspire Use this formula to calculate the Current Loan Balance.
• Algebra Resources for the TN-Nspire The varying balances can be calculated using the Generate Sequence feature.
• Algebra Resources for the TN-Nspire U(n-1)*(1+B2/100/12)+B4 Use this Generate Sequence Formula for Column C.
• Algebra Resources for the TN-Nspire Fill out the Generate Sequence dialogue box.
• Algebra Resources for the TN-Nspire Column C now has all the Current Balance amounts for payments 1 through 360.
• Algebra Resources for the TN-Nspire Knowing what the Current Balance is, we can calculate how much of each monthly payment is interest only.
• Algebra Resources for the TN-Nspire Use a column-level formula to find the percentage of the Current Balance is interest only.
• Algebra Resources for the TN-Nspire Column D shows the amount of the mortgage payment made up of interest only. At the start of the loan, it’s mostly interest.
• Algebra Resources for the TN-Nspire We can now also calculate the amount of each mortgage payment that goes to the principal.
• Algebra Resources for the TN-Nspire Creating a Principal-vs.-Interest scatterplot reveals an interesting pattern.
• Algebra Resources for the TN-Nspire Let lables “principal” and “interest” are based on the Spreadsheet column headings.
• Algebra Resources for the TN-Nspire To see al lof the graph, don’t forget to change the Window settings to Zoom Data.
• Algebra Resources for the TN-Nspire This is the graph of Principal vs. Interest throughout the life of the loan.
• Algebra Resources for the TN-Nspire Finally, we can calculate the Equity, as the loan is gradually repaid.
• Algebra Resources for the TN-Nspire Total Equity is found using this formula. But in 2008, the “increase in value of the house” was a decrease.