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# Presentation 3

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### Presentation 3

1. 1. Petroleum Project Economics Econ210D Presentation 3 Interest and Time Value of Money Week 3
2. 2. <ul><li>Interest remains constant each year. </li></ul><ul><li>Interest is not reinvested </li></ul><ul><li>Interest is calculated by the formula. </li></ul>Simple Interest where: I = Interest, P = Principal, r = interest, n = number of years. Interest and Time Value of Money Week 3
3. 3. <ul><li>Interest is based on principal plus reinvested interest from previous years </li></ul><ul><li>Interest increase each successive year </li></ul>Compound Interest where: P = Principal, r = interest, n = number of years, A = Principal + Interest, Interest and Time Value of Money Week 3
4. 4. Future and Present Value <ul><li>Future Value – the value at some point in the future of a single cash flow or a series of cash flows in the future. </li></ul><ul><li>Present Value – the value today of a single cash flow or a series of cash flows in the future </li></ul><ul><li>Values change over time due to interest </li></ul><ul><li>Interest is based on compound interest </li></ul>Interest and Time Value of Money Week 3
5. 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. 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. 7. Future Value of a Single Cash Flow <ul><li>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? </li></ul>Interest and Time Value of Money Week 3
8. 8. Present Value of a Single Cash Flow <ul><li>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? </li></ul>Interest and Time Value of Money Week 3
9. 9. Annuities – Series of Cash flows <ul><li>An annuity is a series of equal payments at evenly spaced intervals </li></ul><ul><li>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 </li></ul><ul><li>Interest is earned on amounts paid </li></ul>Interest and Time Value of Money Week 3
10. 10. Annuity Due and an Ordinary Annuity – over 3 years <ul><li>Annuity Due </li></ul><ul><li>Ordinary Annuity </li></ul>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. 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. 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. 13. Future Value of an Annuity Due Interest and Time Value of Money Week 3
14. 14. Future Value of an Annuity Due using Formula <ul><li>where </li></ul><ul><li>I = periodic investment </li></ul><ul><li>r = interest rate per period </li></ul><ul><li>n = number of periods </li></ul>Interest and Time Value of Money Week 3
15. 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. 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. 17. Future Value of an Ordinary Annuity Interest and Time Value of Money Week 3
18. 18. Future Value of an Ordinary Annuity using Formula <ul><li>where </li></ul><ul><li>I = periodic investment </li></ul><ul><li>r = interest rate per period </li></ul><ul><li>n = number of periods </li></ul>Interest and Time Value of Money Week 3
19. 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. 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. 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. 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. 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. 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. 25. Present Value of an Annuity Due Interest and Time Value of Money Week 3
26. 26. Present Value of an Annuity Due Using the formula <ul><li>where </li></ul><ul><li>I = periodic investment </li></ul><ul><li>r = interest rate per period </li></ul><ul><li>n = number of periods </li></ul>Interest and Time Value of Money Week 3
27. 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. 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. 29. Present Value of an Ordinary Annuity Interest and Time Value of Money Week 3
30. 30. Present Value of an Ordinary Annuity Using the Formula <ul><li>where </li></ul><ul><li>I = periodic investment </li></ul><ul><li>r = interest rate per period </li></ul><ul><li>n = number of periods </li></ul>Interest and Time Value of Money Week 3
31. 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. 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. 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. 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