1. Lecture 6 Investments Partial Payments Ana Nora Evans Office Hours: Mon 1:00-2:30 Wed 3:30 -5:00 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics College Deadlines Last day to add a class is Tuesday, Sep 6. Last day to drop a class is Wednesday, Sep 7. 2

3. Math 1140 - Financial Mathematics Previous lectures Homework 3 Lecture notes Questions? 3

4. Math 1140 - Financial Mathematics Problem 1 2008 is a leap year! ordinary interest Problem 2 work with months Problem 3 typo in the printed page the net is due in 60 days example 1.4.4 on page 15 Problem 4 The note matures to $40,000 means that the maturity value of the note is $40,000. Problem 5 Not an add-on loan! Problem 6 Today’s lecture Homework 3 4

5. Math 1140 - Financial Mathematics Simple debt instruments Discounting a note Equations of Value Focal date Golden Rule of Finance Terms from last time 5

6. Math 1140 - Financial Mathematics Amount 1 = the sale price of a promissory note at 10% simple interest with the term one year, sold after x days to a third party making 15% simple interest. Amount 2 = maturity value of a 10% simple interest loan with term x days. Correct/Incorrect question A)Amount 1 < Amount 2 B)Amount 2 < Amount 1 C)Amount 1 ≤ Amount 2 D)Amount 2 ≤ Amount 1 E)None of the above (it depends on the principal and the sale date) Pledged quiz – No collaboration 6

7. Math 1140 - Financial Mathematics Amount 1 = the sale price of a promissory note at 10% simple interest with the term one year, sold after x days to a third party making 15% simple interest. Amount 2 = maturity value of a 10% simple interest loan with term x days The correct answer is A. Amount 1 = 1.1P/(1 + 0.15(1 – x/365)) Amount 2 = P( 1 + 0.1x/365) 7

8. Math 1140 - Financial Mathematics Amount 1 = the sale price of a promissory note at 10% simple interest with the term one year, sold after x days to a third party making 10% simple interest. Amount 2 = maturity value of a 10% simple interest loan with term x days. Participation question A)Amount 1 < Amount 2 B)Amount 2 < Amount 1 C)Amount 1 ≤ Amount 2 D)Amount 2 ≤ Amount 1 E)None of the above( It depends on the principal and the sale date.) 8

9. Math 1140 - Financial Mathematics Amount 1 = the sale price of a promissory note at 10% simple interest with the term one year, sold after x days to a third party making 10% simple interest. Amount 2 = a 10% simple interest loan with term x days. 9

10. Math 1140 - Financial Mathematics Goal: predict if an investment will give a good rate of return. The rate of return of an investment is the ratio of money gain or lost relative to the money invested. The net present value (NPV) is the income minus expenses, all moved to the present. The internal rate of return (IRR) is the rate at which the returns and investments make the NPV zero. Investments 10

11. Math 1140 - Financial Mathematics An easier way to think about NPV: use plus sign for income use minus sign for expenses move everything to the present add them all IRR is difficult to calculate. It is difficult to predict accurately the returns. The returns may be irregular. NPV and IRR 11

12. Math 1140 - Financial Mathematics Bob buys an old house for $50,000. He spends $10,000 to fix it and he sells it in six months for $75,000. What is NPV (net present value) at 15% simple interest? What is IRR (internal rate of return)? 12

13. Math 1140 - Financial Mathematics Math can get more complicated If the investment brings returns at two different dates you will need to solve a quadratic equation. If the investment brings returns at three different dates you will need to solve a cubic equation. 13

14. Math 1140 - Financial Mathematics y 2 = dax 2 + bx + c = 0 Quadratic equation formula 14

15. Math 1140 - Financial Mathematics Email Questions 15

16. Math 1140 - Financial Mathematics For a simple interest loan, the borrower is not required to make any payments until the due date. The borrower and the lender may agree how any partial payments will reduce the interest charges. Merchant’s Rule Set the focal date to be the due date. Use an equation of value to determine the balance on the loan. The maturity value is negative. The partial payments (moved to the focal date) are positive. Partial Payments 16

17. Math 1140 - Financial Mathematics Merchant’s Rule 17

18. Math 1140 - Financial Mathematics At the date of a partial payment, the balance is calculated and it becomes the new principal of a simple interest loan with start date the date of the partial payment and due date the original due date. At the due date, the leftover balance is due. The principal is negative. The payments are positive. To calculate the balance: add the principal add the interest add payment United States Rule 18

19. Math 1140 - Financial Mathematics Next time Discount Interest 19

20. Math 1140 - Financial Mathematics Due Wednesday: Read Sections 2.1 and 2.2 Third homework Office Hours : Monday 1:00-2:30 pm Tuesday 3:30-5:00 pm First Exam (max 15 points): 26 September 2011 at 7pm Location to be announced Charge 20