Selected Applications of Mathematics to Finance and Investment (UMAP)

This module is an informal and largely elementary discussion of the background and uses of formulas for finance and investment, including: 1) the basic principles of compound interest and continuous growth; 2) annuities and mortgages; 3) the Rule of 72; 4) formulas for amortization, balloon payments, computation of borrowing potential; 5) calculating APR required by Fedreal Truth-in-Lending; 6) present value of future income and payments; 7) how to exploit leverage in investment; and 8) a model for how to determine when it is optimal to sell an investment. Students understand business and financial concepts and formulas, are able to apply these in practical circumstances, and appreciate the power and usefulness of mathematical concepts and techniques.

Table of Contents:

0. ABOUT THIS MODULE

1. REVIEW OF INTEREST CALCULATIONS: THE DEFINITION OF e; CONTINUOUS GROWTH

2. APPRECIATION

3. THE RULE OF 72

4. ANNUITIES

5. MORTGAGES

6. TRUTH-IN-LENDING

7. DISCOUNTING NOTES AND BONDS

8. FHA POINTS

9. CONTINUOUS APPROXIMATION

10. PRESENT VALUE OF FUTURE PAYMENTS

11. LEVERAGE

12. THE OPTIMAL TIME TO SELL

13. SUMMARY OF FORMULAS

14. SOLUTIONS TO EXERCISES