1. Lecture 32 Outstanding Balance Refinancing Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics The exam 2 was A)Easy B)Just right C)Hard D)Too hard 2

3. Math 1140 - Financial Mathematics Exam 2 Grades 3

4. Math 1140 - Financial Mathematics Assuming you keep working on bonus problems and get a 100 on the project the grade distribution not counting the final, with 100 on the project is: 4

5. Math 1140 - Financial Mathematics Final The final is on December 8, 7-10pm. Location to be announced. There will be 15 problems on the final: 5 questions from chapters 1, 2, 3 5 questions from chapters 4,5 5 problems from chapters 6,7 5

6. Math 1140 - Financial Mathematics The first 10 questions will be similar to exams 1 and 2 (questions from study guide, problems from homework or practice problems). The last 5 problems will be similar to problems from homework 11 trough the last homework. No sample exam, practice problems or study guide will be provided! For practice problems use the textbook! 6

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8. Last time Defined what it means to amortize a debt. We calculated how much of each payment goes to the interest and how much goes to the principal. 8

9. Math 1140 - Financial Mathematics Balance after k th payment: P(1+i) k - R s(k,i) How much of the (k+1) th payment goes to the interest? [P(1+i) k - R s(k,i)](1+i) How much of the (k+1) th payment goes to the principal? R - [P(1+i) k - R s(k,i)](1+i) 9

10. Math 1140 - Financial Mathematics Discount Points A point is 1% of the amount of money being lent. Discount points is an up-front charge on the amount being lent. 10

11. Math 1140 - Financial Mathematics Alice borrows P dollars at rate i per month and p points with monthly payments for n years. What is the real APR? Step 1: Calculate R Step 2: Calculate APR Present value: (1-p)P Rent: R Number of payments: 12n Discount points not added to the principal 11

12. Math 1140 - Financial Mathematics Alice borrows P dollars at rate i per month and p points with monthly payments for n years. What is the real APR if the points are added to the loan? Step 1: Calculate the amount borrowed Step 2: Calculate R Discount points added to the principal 12

13. Math 1140 - Financial Mathematics Alice borrows P dollars at rate i per month and p points with monthly payments for n years. What is the real APR if the points are added to the loan? Step 3: Calculate APR Present value: P Rent: R Number of payments: 12n Discount points added to the principal 13

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15. Math 1140 - Financial Mathematics Outstanding Balance The outstanding balance is the principal still to be paid. 15

16. Math 1140 - Financial Mathematics Prospective Method The outstanding balance at a given time is calculated as the sum of the remaining payments moved to the given time. Given the rent R and the number of payments left m, the outstanding balance is: 16

17. Math 1140 - Financial Mathematics What loan data we need to know to apply the prospective method? - the periodic payment - the number of remaining payments - the interest rate 17

18. Math 1140 - Financial Mathematics Retrospective Method The outstanding balance at a given time is the amount borrowed moved to that time minus the sum of the payments considered at the given time. Given the rent R and the number of payments n, the outstanding balance after the k th payment is 18

19. Math 1140 - Financial Mathematics What loan data we need to know to apply the retrospective method? - the periodic payment - the number of payments made - the amount borrowed - the interest rate 19

20. Math 1140 - Financial Mathematics Do the prospective and retrospective give the same value of the outstanding balance? A)Yes B)No 20

21. Math 1140 - Financial Mathematics How do we decide which method to use? A)We can use either one. B)We always use the prospective method. C)We always use the retrospective method. D)The method used depends on the problem. 21

22. Math 1140 - Financial Mathematics The two methods give the same value if no rounding is allowed. The prospective method is less accurate when all the payments are rounded to the nearest cent. 22

23. Math 1140 - Financial Mathematics Alice takes a $85,000 loan financed at 8.5%(12) for 15 years, with monthly payments. Find the outstanding balance at the end of 8 years. Which method should we apply? The retrospective method. Step 1: Calculate the monthly payment 23

24. Math 1140 - Financial Mathematics Alice takes a $85,000 loan financed at 8.5%(12) for 15 years, with monthly payments. Find the outstanding balance at the end of 8 years. Step 2: Calculate the outstanding balance 24

25. Math 1140 - Financial Mathematics Alice takes a $85,000 loan financed at 8.5%(12) for 15 years, with monthly payments. Find the outstanding balance at the end of 8 years. Use prospective method. The number of payments left is m=12×15-12×8=84. The outstanding balance is: 25

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27. Math 1140 - Financial Mathematics Alice makes monthly payments of $900 for a 12%(12) loan. If she has 10 years left on the loan, what is the outstanding balance on the loan? Which method should we use to calculate the outstanding balance? A)Retrospective B)Prospective C)Either 27

28. Math 1140 - Financial Mathematics Refinancing a Loan Refinancing a loan means to take out a new loan to pay off the existing loan. Why would anyone want to do it? To get a lower rate. To change the term. Shorter term has higher payments. Longer term has smaller payments. 28

29. Math 1140 - Financial Mathematics A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points. Find the interest saved if this loan is refinanced at 7%(12) at the end of the 10 th year, leaving the remaining term unchanged. Step 1: Calculate the payment of the first loan P = $52,000 i = 0.085/12 R = $399.84 29

30. Math 1140 - Financial Mathematics A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points. Find the interest saved if this loan is refinanced at 7%(12) at the end of the 10 th year, leaving the remaining term unchanged. Step 2: Calculate the outstanding balance at the end of the 10 th year using the prospective method P = $52,000 i = 0.085/12 R = $399.84 k = 12×10 OB = $46,072.39 30

31. Math 1140 - Financial Mathematics A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points. Find the interest saved if this loan is refinanced at 7%(12) at the end of the 10 th year, leaving the remaining term unchanged. Step 3: Calculate the payment of the new loan P = $46,072.39 i = 0.07/12 R = $357.2 31

32. Math 1140 - Financial Mathematics A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points. Find the interest saved if this loan is refinanced at 7%(12) at the end of the 10 th year, leaving the remaining term unchanged. Step 4: Calculate the interest saved The interest saved each month is the difference of the two payments. The interest saved is 12×20 ×($399.84-$357.2). 32

33. Math 1140 - Financial Mathematics A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points. This loan is refinanced at 7%(12) at the end of the 10 th year, leaving the remaining term unchanged. How much interest was paid during the 8.5% loan? The interest is calculated as the difference of the sum of all payments and the amount actually borrowed: 120×$399.84-($52,000 - $46,072) 33

34. Math 1140 - Financial Mathematics A home loan for $52,000 is financed at 8.5%(12) for 30 years and no points. This loan is refinanced at 7%(12) at the end of the 10 th year, leaving the remaining term unchanged. How much interest was paid during the 7% loan? The interest is calculated as the difference of the sum of all payments and the amount actually borrowed: 12×20×$357.2 -$46,072 34

35. Math 1140 - Financial Mathematics Wednesday Read sections 6.3 and 6.4 Nov 11 (next Friday) Project Progress Report Dec 8 (a little over a month) FINAL!!!! Charge 35