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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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