1. Lecture 27 Amortization of Debts Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics A)I plan to come to office hours Wed 10:30-11:30 B)I plan to come to office hours Wed 3-4 C)I plan to come to office hours Thu 3-4 D)I don’t plan to come to office hours E)I started to study and I will have questions for you on Friday. 2

3. Math 1140 - Financial Mathematics Last time we discussed perpetuities. Today, we start chapter 6. We will talk about amortization of debts and amortization schedules. 3

4. Math 1140 - Financial Mathematics A perpetuity is an annuity with A)Unequal payments. B)Different compounding period and rent period. C)A finite number of payments. D)Infinitely many payments. E)Payments at the end of the rent period. 4

5. Math 1140 - Financial Mathematics Perpetuity A perpetuity is an annuity with infinitely many payments. The periodic payment, R, is the interest earned during the previous rent period. The present value is located one period before the first payment. 5

6. Math 1140 - Financial Mathematics Perpetuity Due The present value is located at the first payment. 6

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8. Exam 2 – 7-9pm, Wed, 2 Nov 2011 Make-up – 7-9am, Thu, 3 Nov 2011 Sign-up for make-up before 5pm today!!! 8

9. Math 1140 - Financial Mathematics Suppose that you agree to loan $20,000 from your grandma, to be repaid with 48 monthly payments. The two of you agree on a nominal rate of 9% convertible monthly, and that the first payment should be due a month from now. How large should each monthly payment be? 9

10. Math 1140 - Financial Mathematics The sequence of payments is an ordinary annuity. The payment, R, is determined by solving the equation: the present value of the ordinary annuity is equal to the amount borrowed, P. 10

11. Math 1140 - Financial Mathematics Suppose that you agree to loan $20,000 from your grandma, to be repaid with 48 monthly payments. The two of you agree on a nominal rate of 9% convertible monthly, and that the first payment should be due a month from now. How large should each monthly payment be? We have: P = $20,000 n = 48 i = 0.09/12 We want to calculate R. 11

12. Math 1140 - Financial Mathematics What if instead of setting the focal point one period before the first payment, we set the focal point at the last payment? A)We get the same result. B)We get a different result. 12

13. Math 1140 - Financial Mathematics At the last payment P is worth P(1+i) n. At the last payment all the payments are worth 13

14. Math 1140 - Financial Mathematics We need to solve for R 14

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16. Math 1140 - Financial Mathematics Terms The cash price of an object is the price actually paid for that object. Sometimes, the lender requires the borrower to pay some part of the object and only borrow the rest of the money. This payment is called down payment. The borrower borrows only the difference between the cash price and the down payment. 16

17. Math 1140 - Financial Mathematics To amortize a debt means to pay a sequence of equal-size payments at equal time intervals. Each payment has two components 1. the interest due on the balance right after the previous payment 2. part of the principal 17

18. Math 1140 - Financial Mathematics The principal decreases by: A)Equal amount each month. B)Smaller and smaller amounts each month. C)Bigger and bigger amounts each month. 18

19. Math 1140 - Financial Mathematics Today before 5 pm Email me if you want to take the make-up. Friday Homework 9 due Friday’s class is in Rice Hall, fourth floor. Exam 2 Wed, 2 Nov 2011, 7-9pm Make-up Thu, 3 Nov 2011, 7-9am Charge 19