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CTC 475 Review

CTC 475 Review . Interest/equity breakdown What to do when interest rates change Nominal interest rates Converting nominal interest rates to regular interest rates Converting nominal interest rates to effective interest rates. CTC 475 . Changing interest rates to match cash flow intervals.

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CTC 475 Review

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  1. CTC 475 Review • Interest/equity breakdown • What to do when interest rates change • Nominal interest rates • Converting nominal interest rates to regular interest rates • Converting nominal interest rates to effective interest rates

  2. CTC 475 Changing interest rates to match cash flow intervals

  3. Objectives • Know how to change interest rates to match cash flow intervals • Understand continuous compounding

  4. What if the cash flow interval doesn’t match the compounding interval? • Cash flows occur more frequently than the compounding interval • Compounded quarterly; deposited monthly • Compounded yearly; deposited daily • Cash flows occur less frequently than the compounding interval • Compounded monthly; deposited quarterly • Compounded quarterly; deposited yearly

  5. Cash flows occur more frequently than the compounding interval • Use ieff=(1+i)m-1 and solve for i • Note that a nominal interest rate must first be converted into ieff or i before using the above equation

  6. Cash flows occur less frequently than the compounding interval • Use ieff=(1+i)m-1 and solve for ieff • Note that a nominal interest rate must first be converted into ieff or i before using the above equation

  7. Case 1 Example • Cash flows occur more frequently than compounding interval • Solve for i

  8. Example--Cash flows are more frequent than compounding interval (solve for i) • 8% per yr compounded qtrly (recognize this as a nominal interest rate and convert to 2% per quarter compounded quarterly) • Individual makes monthly deposits (cash flows are more frequent than compounding interval) • We want an interest rate of ?/month compounded monthly • Use ieff=(1+i)m-1 and solve for i

  9. Example-Continued • Use ieff=(1+i)m-1 and solve for i • .02=(1+i)3-1 (m=3; 3 months per quarter) • 1.02 =(1+i)3 • Raise both sides by 1/3 • i=.662% per month compounded monthly

  10. Case 2 Example • Cash flows occur less frequently than compounding interval • Solve for ieff

  11. Example--Cash flows are less frequent than compounding interval (solve for ieff) • 8% per yr compounded qtrly (recognize this as a nominal interest rate and convert to 2% per quarter compounded quarterly) • Individual makes semiannual deposits (cash flows are less frequent than compounding interval) • We want an equivalent interest rate of ?/semi compounded semiannually • Use ieff=(1+i)m-1 and solve for ieff

  12. Example-Continued • Use ieff=(1+i)m-1 and solve for ieff • ieff =(1+.02)2-1 (m=2; 2 qtrs. per semi) • ieff =4.04% per semi compounded semiannually

  13. What is Continuous Compounding? • Appendix D

  14. Continuous Compounding

  15. Continuous Compounding • As the time interval gets smaller and smaller (eventually approaching 0) you get the equation: • ieff=er-1 • Therefore the effective interest rate for 8% per year compounded continuously = e.08-1=8.3287%

  16. Continuous Compounding • If the interest rate is 12% compounded continuously, what is the effective annual rate? • ieff=er-1 • ieff= e.12-1=12.75%

  17. Continuous Compounding • Continuous compounding factors can be found in Appendix D of your book (for r=8,10 and 20% • Equations can be found on page 650 • Always assume discrete compounding (use Appendix C) unless the problem statement specifically states continuous compounding

  18. Continuous Compounding; Single Cash Flow • If $2000 is invested in a fund that pays interest @ a rate of 10% per year compounded continuously, how much will the fund be worth in 5 years? • Method 1-Use book factors • F=P(F/Pr,n)=2000(F/P10,5)=2000(1.6487) • F=$3,297

  19. Continuous Compounding; Single Cash Flow • If $2000 is invested in a fund that pays interest @ a rate of 10% per year compounded continuously, how much will the fund be worth in 5 years? • Method 2-Use equation • F=P*ern=e(.1*5)=2000(1.6487) • F=$3,297

  20. Continuous Compounding; Single Cash Flow • If $2000 is invested in a fund that pays interest @ a rate of 10% per year compounded continuously, how much will the fund be worth in 5 years? • Method 3-Find effective interest rate • ieff=er-1 = e.10-1 = 10.52% • F=P(1+i)5 = 2000(1.1052)5 = $3,298

  21. Continuous Compounding; Uniform Series • $1000 is deposited each year for 10 years into an account that pays 10%/yr compounded continuously. Determine the PW and FW. • P=A(P/A10,10)=1000(6.0104)=$6,010 • F=A(F/A10,10)=1000(16.338) =$16,338 • Or F=P(F/P10,10)=6010(2.7183)=$16,337

  22. Continuous Compounding • The continuous compounding rate must be consistent with the cash flow intervals (i.e. 12% per year compounded continuously won’t work with semiannual deposits) • Must change r to 6% per semi compounded semiannually • Equation is (r/n) where r is the annual rate and n is the # of intervals in a year

  23. Next lecture • Methods of Comparing Investment Alternatives

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