The document discusses concepts related to interest and the time value of money, including simple vs compound interest, future value and present value calculations, and calculations related to annuities. It provides examples of calculating future and present values for single cash flows and annuities using formulas, and asks questions requiring the use of these formulas.

1. Petroleum Project Economics Econ210D Presentation 3 Interest and Time Value of Money Week 3

2. Interest remains constant each year. Interest is not reinvested Interest is calculated by the formula. Simple Interest where: I = Interest, P = Principal, r = interest, n = number of years. Interest and Time Value of Money Week 3

3. Interest is based on principal plus reinvested interest from previous years Interest increase each successive year Compound Interest where: P = Principal, r = interest, n = number of years, A = Principal + Interest, Interest and Time Value of Money Week 3

4. Future and Present Value Future Value – the value at some point in the future of a single cash flow or a series of cash flows in the future. Present Value – the value today of a single cash flow or a series of cash flows in the future Values change over time due to interest Interest is based on compound interest Interest and Time Value of Money Week 3

5. where: F = Future value I = Investment/Principal r = rate of interest (for each time period) n = number of time periods. Future Value Interest and Time Value of Money Week 3

6. Present Value where: P = Present value I = Investment/Principal r = rate of interest (for each time period) n = number of time periods. Interest and Time Value of Money Week 3

7. Future Value of a Single Cash Flow An investor deposits $100 into an account which offers 12% p.a. compound interest. What is the value of the investment at the end of 3 years? Interest and Time Value of Money Week 3

8. Present Value of a Single Cash Flow An investor is supposed to receive $100 in 3 years time. If the rate of compound interest is 12% p.a. what is the present value of the amount? Interest and Time Value of Money Week 3

9. Annuities – Series of Cash flows An annuity is a series of equal payments at evenly spaced intervals The payments occur at the beginning of each period for an annuity due while they occur at the end of each period for an ordinary annuity Interest is earned on amounts paid Interest and Time Value of Money Week 3

10. Annuity Due and an Ordinary Annuity – over 3 years Annuity Due Ordinary Annuity Jan 1 st 2009 $100 $100 $100 $100 $100 $100 Jan 1 st 2009 Jan 1 st 2010 Jan 1 st 2011 Dec 31 st 2011 Dec 31 st 2009 Dec 31 st 2010 Dec 31 st 2011 Interest and Time Value of Money Week 3

11. Future Value of an Annuity Due At the beginning of each year an investor deposits $100 into an account which offers 12% p.a. compund interest. What is the value of the investment at the end of 3 years? Interest and Time Value of Money Week 3

12. Future Value of an Annuity Due Interest and Time Value of Money Week 3 Time Year Amount Workings Future Value Jan 1st 2009 0 $100 $140 Jan 1st 2010 1 $100 $125 Jan 1st 2011 2 $100 $112 Dec 31st 2011 3 $0 $0 Total $300 $378

13. Future Value of an Annuity Due Interest and Time Value of Money Week 3

14. Future Value of an Annuity Due using Formula where I = periodic investment r = interest rate per period n = number of periods Interest and Time Value of Money Week 3

15. Future Value of an Ordinary Annuity At the end of each year an investor deposits $100 into an account which offers 12% p.a. compound interest. What is the value of the investment at the end of 3 years? Interest and Time Value of Money Week 3

16. Future Value of an Ordinary Annuity Interest and Time Value of Money Week 3 Time Year Amount Workings Future Value Jan 1st 2009 0 $0 $0 Dec 31st 2009 1 $100 $125 Dec 31st 2010 2 $100 $112 Dec 31st 2011 3 $100 $100 Total $300 $337

17. Future Value of an Ordinary Annuity Interest and Time Value of Money Week 3

18. Future Value of an Ordinary Annuity using Formula where I = periodic investment r = interest rate per period n = number of periods Interest and Time Value of Money Week 3

19. Question 1 At the beginning of each year an investor deposits $10,000 into an account which offers 10% p.a. compound interest. What is the value of the investment at the end of 4 years? Interest and Time Value of Money Week 3

20. Question 2 At the end of each year an investor deposits $2,000 into an account which offers 2% p.a. compound interest. What is the value of the investment at the end of 5 years? Interest and Time Value of Money Week 3

21. Question 3 At the end of each quarter an investor deposits $400 into an account which offers 12% p.a. compound interest. What is the value of the investment at the end of 1 year? Interest and Time Value of Money Week 3

22. Question 4 At the beginning of each month an investor deposits $100 into an account which offers 12% p.a. compound interest. What is the value of the investment at the end of 6 months? Interest and Time Value of Money Week 3

23. Present Value of an Annuity Due At the beginning of each year an investor deposits $100 into an account which offers 12% p.a. compund interest. What is the present value of the investment? Interest and Time Value of Money Week 3

24. Present Value of an Annuity Due Interest and Time Value of Money Week 3 Time Year Amount Workings Present Value Jan 1st 2009 0 $100 $100 Jan 1st 2010 1 $100 $89 Jan 1st 2011 2 $100 $80 Dec 31st 2011 3 $0 $0 Total $300 $269

25. Present Value of an Annuity Due Interest and Time Value of Money Week 3

26. Present Value of an Annuity Due Using the formula where I = periodic investment r = interest rate per period n = number of periods Interest and Time Value of Money Week 3

27. Present Value of an Ordinary Annuity At the end of each year for 3 years an investor deposits $100 into an account which offers 12% p.a. compound interest. What is the present value of the investment? Interest and Time Value of Money Week 3

28. Present Value of an Ordinary Annuity Interest and Time Value of Money Week 3 Time Year Amount Workings Present Value Jan 1st 2009 0 $0 $0 Dec 31st 2009 1 $100 $89 Dec 31st 2010 2 $100 $80 Dec 31st 2011 3 $100 $71 Total $300 $240

29. Present Value of an Ordinary Annuity Interest and Time Value of Money Week 3

30. Present Value of an Ordinary Annuity Using the Formula where I = periodic investment r = interest rate per period n = number of periods Interest and Time Value of Money Week 3

31. Question 5 At the beginning of each year an investor deposits $10,000 into an account which offers 10% p.a. compound interest. What is the present value of the investment if this is done over 4 years? Interest and Time Value of Money Week 3

32. Question 6 At the end of each year for 5 years an investor deposits $2,000 into an account which offers 2% p.a. compound interest. What is the present value of the investment? Interest and Time Value of Money Week 3

33. Question 7 At the end of each quarter an investor deposits $400 into an account which offers 12% p.a. compound interest. What is the present value of the investment if this is done over 1 year? Interest and Time Value of Money Week 3

34. Question 8 At the beginning of each month for 6 months an investor deposits $100 into an account which offers 12% p.a. compound interest. What is the present value of the investment? Interest and Time Value of Money Week 3