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

2. Algebra Resources for the TN-Nspire
Media4Math includes a variety of free and
premium resources, including short video
tutorials on the Nspire, Math in the News, and
other tutorials.

3. Algebra Resources for the TN-Nspire
In this presentation we will focus on our DVD
Library, Algebra Applications.

4. Algebra Resources for the TN-Nspire
Volume 1 Volume 2
1. Linear Functions 6. Functions and
2. Quadratic Functions Relations
3. Variables and 7. Exponential Functions
Equations 8. Logarithmic Functions
4. Inequalities 9. Rational Functions
5. Data Analysis 10. Systems of Equations

5. Algebra Resources for the TN-Nspire
Algebra Applications: Data Analysis focuses on
the housing crisis of 2008.

6. Algebra Resources for the TN-Nspire
The impact of the housing crisis was a steep drop
in the stock market.

7. Algebra Resources for the TN-Nspire
The value of houses on the market began to go
down and some had trouble keeping up with
suddenly higher mortgage payments.

8. Algebra Resources for the TN-Nspire
As a result, the number of foreclosures began to
increase dramatically.

9. Algebra Resources for the TN-Nspire
To get a better understanding of the housing
crisis, we start with what a mortgage is.

10. Algebra Resources for the TN-Nspire
We use the TI-Nspire to explore different
mortgage scenarios and also construct an
amortization table.

11. Algebra Resources for the TN-Nspire
We start by opening a Spreadsheet window and
labeling three cells for the loan amount, the
interest rate, and the total number of payments.

12. Algebra Resources for the TN-Nspire
We input the values shown, and we use the
Nspire’s Time Value of Money function to
calculate the mortgage amount.

13. Algebra Resources for the TN-Nspire
The TVMPMT function takes six values: the
number of payments, interest, loan amount,
future value, and payments and compoundings
per year.

14. Algebra Resources for the TN-Nspire
The future value is set to zero since
we’re calculating full repayment of
the loan.

15. Algebra Resources for the TN-Nspire
The result is the monthly mortgage
payment, set as a negative value.

16. Algebra Resources for the TN-Nspire
We can now calculate the full value
of the loan, principal plus all interest
payments.

17. Algebra Resources for the TN-Nspire
So, for this mortgage the loan
repayment is nearly twice the value
of the original loan amount.

18. 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.

19. 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.

20. Algebra Resources for the TN-Nspire
The Current Loan Balance is made up
of these three values.

21. Algebra Resources for the TN-Nspire
Use this formula to calculate the
Current Loan Balance.

22. Algebra Resources for the TN-Nspire
The varying balances can be
calculated using the Generate
Sequence feature.

23. Algebra Resources for the TN-Nspire
U(n-1)*(1+B2/100/12)+B4
Use this Generate Sequence Formula
for Column C.

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Fill out the Generate Sequence
dialogue box.

25. Algebra Resources for the TN-Nspire
Column C now has all the Current
Balance amounts for payments 1
through 360.

26. Algebra Resources for the TN-Nspire
Knowing what the Current Balance is,
we can calculate how much of each
monthly payment is interest only.

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Use a column-level formula to find the
percentage of the Current Balance is
interest only.

28. 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.

29. Algebra Resources for the TN-Nspire
We can now also calculate the
amount of each mortgage payment
that goes to the principal.

30. Algebra Resources for the TN-Nspire
Creating a Principal-vs.-Interest
scatterplot reveals an interesting
pattern.

31. Algebra Resources for the TN-Nspire
Let lables “principal” and “interest”
are based on the Spreadsheet column
headings.

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To see al lof the graph, don’t forget to
change the Window settings to Zoom
Data.

33. Algebra Resources for the TN-Nspire
This is the graph of Principal vs.
Interest throughout the life of the
loan.

34. Algebra Resources for the TN-Nspire
Finally, we can calculate the Equity,
as the loan is gradually repaid.

35. 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.