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Recitation 05

Recitation 05. Announcements. Investment Exercise You must put at least one transaction for momentum and contrarian strategy by 5:00 pm Monday. Announcements. Online Quiz 3 Starts at 8:00 am on Monday, Sep 23rdand is due 5:00pm Friday , Sep 27 th Covers

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Recitation 05

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  1. Recitation 05

  2. Announcements • Investment Exercise • You must put at least one transaction for momentum and contrarian strategy by 5:00 pm Monday

  3. Announcements • Online Quiz 3 • Starts at 8:00 am on Monday, Sep 23rdand is due 5:00pm Friday, Sep 27th • Covers • Hedge Fund Protection in Bear Markets for the Retail Investor  (page 68) • Linking the Pieces Together—and Then Some  (page 71)

  4. Frequency of Compounding

  5. Frequency of Compounding • In reality you will probably encounter • Semi-annual compounding • Quarterly compounding • Monthly compounding • Daily compounding • Implications? • It speeds up the exponential growth

  6. Frequency of Compounding: Example • You deposit $1,000 in an account that pays 12% interest, compounded quarterly. How much is in the account after 8 years?

  7. Frequency of Compounding: Example Given: Steps:

  8. Importance of Frequency Given:

  9. Effective Annual Rates • It is also necessary to adjust interest rates for comparison purposes • You cannot directly compare two nominal rates that have different compounding frequencies • Effective Annual Rates that consider the frequency of compounding need to be used

  10. Effective Annual Rates: Example • What is the effective annual rate of interest for a loan that has an 18% annual percentage rate, compounded monthly?

  11. Effective Annual Rates: Example Given: Steps:

  12. Annuities

  13. Annuities • Annuities are a series of multiple cash flows • Equal payments • Equidistant payments • Application • Mortgages • Retirement savings plans • Insurance

  14. Annuity Problem Variables • Future Value of Annuity (FVA) • Present Value of Annuity (PVA) • Cash flow amount (CF) • Number of cash flows (n) • Interest Rate (i) • Future Value Factor of Annuity (FVFA) • Compound Factor • Present Value Factor of Annuity (PVFA) • Discount Factor

  15. Future Value of Annuity • You took out a loan for a car, that you will pay in 5 annual installments of $1000, with interest rate of 5% .What would be total amount you paid(FV)?

  16. Calculating Annuity Future Value of Annuity = $5525.64 Or use Annuity formula :

  17. Annuity Equations • Compounding • Discounting

  18. Important Annuity Feature • PVA – is always located one period before first CF • FVA – is always located at the last CF period CF CF CF CF CFCFCF PVA FVA

  19. Annuity Example • You took out a loan that you will be making payments of $100 for next 5 years with interest rate of 5%. • What is the Present Value of the loan (amount you borrowed)? • What is the Future Value of the loan (amount you will pay back)?

  20. Annuity Example: Visualize • Identify individual cash flows 100 100 100 100 100 0 1 2 3 4 5

  21. Annuity Example Given: Steps:

  22. Annuity Example

  23. Annuity Example • What happens when we have two annuities? First cash flow of $300 lasts for 3 periods starting from period 2, and second cash flow of $500 starts right after the first one and lasts for another 3 periods What is the value of these cash flows at t=0, i=5%?

  24. Annuity Example: Visualize • Identify individual cash flows 300 300 300 500 500 500 0 1 2 3 4 5 6 7

  25. Annuity Example Given: Steps:

  26. Annuity Example

  27. Annuity Example • How much would you have to deposit each month in an account that earns 4% interest (compounded annually) if you want to have $20,000 four years from now? (your first deposit will be one month from now and your last deposit will be 48 months from now)

  28. Annuity Example Given: Steps:

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