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CTC 475 Review

CTC 475 Review. Time Value of Money Future/Present Direct/Indirect Fixed/Variable Average/Marginal/Opportunity. CTC 475. Interest and Single Sums of Money. Objectives. Work problems using both simple and compound interest Determine the future worth of a single sum

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CTC 475 Review

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  1. CTC 475 Review Time Value of Money Future/Present Direct/Indirect Fixed/Variable Average/Marginal/Opportunity

  2. CTC 475 Interest and Single Sums of Money

  3. Objectives • Work problems using both simple and compound interest • Determine the future worth of a single sum • Determine the present worth of a single sum • Know how to solve for i or n

  4. Time Value of Money • Value of a given sum of money depends on when the money is received

  5. Which would you prefer?

  6. Which Would you Prefer?

  7. Money Has a Time Value • Money at different time intervals is worth different amounts • Time (or year at which cash flow occurs) must be taken into account

  8. Simple vs Compound Interest • If $1,000 is deposited in a bank account, how much is the account worth after 5 years, if the bank pays • 3% per year ---simple interest? • 3% per year ---compound interest?

  9. Simple vs Compound Interest

  10. Simple Interest Equation Simple—every year you earn 3% ($30) on the original $1000 deposited in the account at year 0 Fn=P(1+i*n) Where: F=Futureamount at year n P=Present amount deposited at year 0 i=interest rate

  11. Compound Interest Equation Compound—every year you earn 3% on whatever is in the account at the end of the previous year Fn=P(1+i)n Where: F=Futureamount at year n P=Present amount deposited at year 0 i=interest rate

  12. Example-Simple vs Compound An individual borrows $1,000. The principal plus interest is to be repaid after 2 years. An interest rate of 7% per year is agreed on. How much should be repaid using simple and compound interest? Simple: F=P(1+i*n)=1000(1+.07*2)=$1,140 Compound: F=P(1+i)n=1000(1.07)2=$1,144.90

  13. Simple or Compound? In practice, banks usually pay compound interest Unless otherwise stated assume compound interest is used

  14. Factor Form Previous slide shows equation form for compound interest The factor form is a shortcut used to find answers faster from tables in the book

  15. Factor Form • F=P(F/Pi,n) Find the future worth (F) given the present worth (P) at interest rate (i) at number of interest periods (n) Future worth=Present worth * factor Note that the factor = (1+i)n

  16. Example of Find F given P problem-Equation vs Factor An individual borrows $1,000 at 6% per year compounded annually. If the loan is to be repaid after 5 years, how much will be owed? Equation: F=P(1+i)n=1000(1.06)5=$1,338.20 Factor: F= P(F/P6,5)=1000(1.3382)=$1,338.20 Note that the factor comes from Table 11 from your book (page 449). Also note that the factor = (1.06)5 =1.3382

  17. Find P given F Can rewrite F=P(1+i)n equation to find P given F: Equation Form: P=F/(1+i)n =F*(1+i)-n OR Factor Form: P=F(P/Fi,n)

  18. Example of Find P given F problem: Equation vs Factor What single sum of money does an investor need to put away today to have $10,000 5 years from now if the investor can earn 6% per year compounded yearly? Equation: P=F*(1+i)-n=10,000(1.06)-5 =$7,473 Factor: P=F(P/Fi,n)=1000(0.7473)=$7,473 Note that the factor comes from Table 11 out of your book. Also note that the factor = (1.06)-5 =0.7473. Also note that the P/F factor is the reciprocal of the F/P factor

  19. Example of Find P given F If you wish to accumulate $2,000 in a savings account in 2 years and the account pays interest at a rate of 6% per year compounded annually, how much must be deposited today? F=$2,000 P=? i=6% per year compounded yearly n=2 years Answer: $1,780

  20. Relationship between P and F • F occurs n periods after P • P occurs n periods before F

  21. Find i given P/F/n Can rewrite F=P(1+i)n equation and solve for i: i=(F/P)(1/n)-1 15 years ago a textbook costs $25.00. Today it costs $50.00. What is the inflation rate per year compounded yearly? Answer: 4.73%

  22. Find n given P/F/i Can rewrite F=P(1+i)n equation and solve for n How long (to the nearest year) does it take to double your money at 7% per year compounded yearly?

  23. Solve for nMethod 1-Solve directly • F=P(1+i)n • Let P=D; therefore F=2D (double the value) • 2D=D(1.07) n • 2=1.07 n • log 2 = n*log(1.07) • n=10.2 years

  24. Solve for nMethod 2-Trial & Error

  25. Solve for nMethod 3-Use factors in back of book • F/P=2 • @ n=10; F/P=1.9727 • @ n=11; F/P=2.1049 • To the nearest year; n=10 • Interpolate to get n=10.2

  26. More than one cash flow?

  27. Series of single sum cash flows How much must be deposited at year 0 to withdraw the following cash amounts? (i=2% per year compounded yearly)

  28. Cash Flow Series (Present Worth) P(at year 0)=: 1000(P/F2,1)+ 3000(P/F2,2)+ 2000(P/F2,3)+ 3000(P/F2,4)

  29. Series of single sum cash flows How much would an account be worth at the end of year 4 if the following cash flows were deposited? (i=2% per year compounded yearly)

  30. Cash Flow Series (Future worth) F(at year 4)=: 1000(F/P2,3)+ 3000(F/P2,2)+ 2000(F/P2,1)+ 3000(F/P2,0)

  31. Next lecture • Uniform Series

  32. BREAK

  33. Student Presentations

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