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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:

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CTC 475 Review

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  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%)

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