STAT6181049 - Session 4 - Lecture Notes Financial.pptx

lecture notes

1. STAT6181049: Financial and Actuarial Science Asysta Amalia Pasaribu , S.Si ., M.Si . Department of Statistics, School of Computer Science Bina Nusantara University Email: [email protected] Solving Problems in Interest

2. Outline Deposits and Withdrawals: Cash Flow Problems Doubling Time Equations of Value at any Time Finding the Rate of Interest Fractional Time Periods Measuring Time Periods: Simple Interest and Fractional Time Periods Unknown Time

3. Measuring Time Periods: Simple Interest and Fractional Time Periods

4. Method One: Exact This method uses the exact number of days and calculates t based on the assumption that there are 365 days in a year.

5. Method Two: Ordinary Simple Interest This method uses the exact number of days and calculates t based on the assumption that there are 365 days in a year.

6. Fractional Time Periods This method uses the exact number of days and calculates t based on the assumption that there are 365 days in a year.

7. Fractional Time Periods

8. Fractional Time Periods

9. Fractional Time Periods

10. Fractional Time Periods

11. Fractional Time Periods

12. Example

13. Latihan soal The Squidward purchase a home for $450,000 and finance $285,000. The interest rate is a nominal 8% convertible quarterly. The Squidward close on September 12, 2007, and must pay simple interest on the amount financed for the remaining days in September. How much do they owe at closing? The Spongebob purchase a home for $430,000 and finance $286,000. The interest rate is a nominal 9% convertible quarterly. The Spongebob close on October 14, 2007, and must pay simple interest on the amount financed for the remaining days in October. How much do they owe at closing?

14. Equations of Value at any Time

15. Equations of Value at any Time

16. Equations of Value at any Time

17. Equations of Value at any Time In return the promise of a payment of $700 at the end of eight years, a person agrees to pay $100 now, $200 at the end of five years, and to make one further payment at the end of ten years. What is the required final payment if the nominal rate of annual interest is 6.2% compounded semiannually? In return the promise of a payment of $700 at the end of eight years, a person agrees to pay $200 now, $100 at the end of five years, and to make one further payment at the end of ten years. What is the required final payment if the nominal rate of annual interest is 6.2% compounded semiannually?

18. Unknown Time

19. Method of Equated Time

20. Doubling Time

21. Doubling Time

22. Doubling Time

23. Finding the Rate of Interest

24. Finding the Rate of Interest

25. Finding the Rate of Interest

26. Finding the Rate of Interest

27. Deposits and Withdrawals: Cash Flow Problems

28. Deposits and Withdrawals: Cash Flow Problems

29. Deposits and Withdrawals: Cash Flow Problems

30. STAT6181049: Financial and Actuarial Science Asysta Amalia Pasaribu , S.Si ., M.Si . Department of Statistics, School of Computer Science Bina Nusantara University Email: [email protected] Annuities

31. Annuities An annuity is a sequence of payments made at agreed upon intervals of time. We will begin our study of annuities with the case in which the payments are equal in value and are made at equal periods of time for an agreed upon period of time. For example, an annuity which pays $100 every month for three years. This is called a fixed term level payment annuity. The word term refers to the total length of time payments are to be made. The term of an annuity can be stated in years or as the number of payments. Thus an annuity which provides monthly payments of three years has a term of three years or thirty-six months. The appropriate term to use depends on the conversion period for the interest rate.

32. Annuities Rent, mortgage payments, and retirement plans are all examples of annuities. Additionally, bonds often provide periodic interest payments. Thus, a bond can be thought of as a form of annuity. While annuities, loans, and bonds are very similar, the sorts of questions we need to solve are very different. As a result, each instrument will get its own chapter.

33. Fixed Term Annuities-Immediate with Constant Payments