1 / 21

CTC 475 Review

CTC 475 Review. Gradient Series Find P given G Find A given G Rules: P occurs two periods before the first G n equals the number of cash flows + 1 First cash flow is G. CTC 475 Review. Geometric Series Find P given A 1 , i and j Find F given A 1 , i and j Rules:

cady
Télécharger la présentation

CTC 475 Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CTC 475 Review Gradient Series • Find P given G • Find A given G Rules: • P occurs two periods before the first G • n equals the number of cash flows + 1 • First cash flow is G

  2. CTC 475 Review Geometric Series • Find P given A1, i and j • Find F given A1, i and j Rules: • P occurs one period before A1 • F occurs the same time as the last cash flow • n equals the number of cash flows • First cash flow is A1

  3. CTC 475 Interest/equity, Changing interest rates and Effective interest rates

  4. Objectives • Know how to determine equity (principal) and interest on borrowed money • Know how to recognize and solve problems when interest rates change • Know how to calculate effective interest rates

  5. Principle and Interest • An individual borrows $10,000 and agrees to pay it back in 5 equal payments at an interest rate of 6% per year compounded yearly. • A=P(A/P6,5) • A=$10,000(.2374) • A=$2,374 • Total=$11,870

  6. Interest/Equity

  7. Methods for borrowing money • Periodic payment of interest with all principle being repaid at end of repayment period. • Uniform payment of principle. • Uniform payment (principle and interest). • Pay nothing until end of repayment period.

  8. Example ProblemMethod 1-4 • Borrowed amount = $40K • 18% per year compounded annually • Repayment period-5 years

  9. Method 1-Pay Interest Periodically

  10. Method 2-Pay Principal Periodically

  11. Method 3-Uniform Payment

  12. Method 4-Pay All at End

  13. Changing Interest Rates • $1000 is deposited into an account. The account pays 4% per year for 3 years and 5% per year for 4 years. How much is the account worth at the end of year 7? F (3)=1,000(1.04)3=$1,124.86 F(7) =$1,124.86(1.05)4=$1,367 or F=$1,000(1.04)3(1.05)4=$1,367

  14. Multiple Compounding Periods in a Year • 12% compounded quarterly is equivalent to 3% every 3 months • 12% is the nominal interest rate (r-mixed) • 3% is the interest rate per interest period (i-not mixed) • 3 months is the duration period • m is the number of compounding periods per year (m=4 quarters per year) • i = r/m =12%/4=3%

  15. Remember Can only use tools if all periods match 3% per quarter compounded quarterly for 20 quarters

  16. Example If $1000 is borrowed at an interest rate of 12% compounded quarterly then what is the amount owed after 5 years? Change nominal rate: 12/4=3% per quarter comp. quarterly Change periods to quarters: 5yrs=20 quarters F=$1,000(1.03)20=$1806 Not: $1,000(1.12)5=$1762

  17. Example If $1000 is borrowed at an interest rate of 8% compounded quarterly then what is the amount owed after 1 year? Change nominal rate: 8/4=2% per quarter comp. quarterly Change periods to quarters: 1yr=4 quarters F=$1,000(1.02)4=$1,082.40 If the interest rate had been 8.24% per year compounded yearly you would have gotten the same result (definition of effective interest rate, ieff)

  18. Effective Interest Rate • ieff=(1+r/m)m-1 • ieff=(1+i)m-1 • ieff=(1+.08/4)4-1=.0824 (8.24%) • ieff=(1+.02)4-1 = .0824 (8.24%)

  19. Example • An individual borrowed $1,000 and paid off the loan with interest after 4.5 years. The amount paid was $1500. What was the effective annual interest rate for this transaction? • i=? • ieff=? • n=4.5 years • m=9 (half-year increments) • $1500=$1000(1+i)9 • i=4.6% per 6 months compounded every 6 months =9.2% per year compounded every 6 months • ieff=(1.046)2-1 • ieff=9.43% per year compounded yearly

  20. Next lecture • What to do when your cash flow interval doesn’t occur at the same time as the compound interval • 3% per yr compounded qtrly; cash flows are monthly

  21. Practice Determine the effective annual interest rate: 6%/year, compounded monthly (6.17%) 6%/year, comp. hourly (6.18%) 2%/year, comp. semiannually (2.01%) 1%/month, comp. monthly (12.68%) 5%/year, comp. daily (5.13%) 2%/quarter, comp. monthly (8.30%)

More Related