1. www.ischool.drexel.edu INFO 630 Evaluation of Information Systems Dr. Jennifer Booker Week 6 – Chapters 4-6 1INFO630 Week 6

2. www.ischool.drexel.edu The Business Decision-Making Process Slides adapted from Steve Tockey – Return on Software 2INFO630 Week 6

3. www.ischool.drexel.edu Overview For any technical problem –Usually many viable technical solutions Goal for technical person is to: –Make the most of the organization limited resources –By choosing the solutions that maximizes the return on the software investment Why do care about this? –Possibly large difference is cost and income for the different solutions –How come? 3INFO630 Week 6

4. www.ischool.drexel.edu Business Decision-making Process Outline 4INFO630 Week 6

5. www.ischool.drexel.edu This same process applies at all levels of business decision –Smaller scale decisions can be done less formally The process is more fluid than implied –Steps can be overlapped or parallel –Steps can be done in different orders Comments on the Process 5INFO630 Week 6

6. www.ischool.drexel.edu The Business Decision Making Process 6INFO630 Week 6

7. www.ischool.drexel.edu Understand the Real Problem Obvious –but often overlooked In software, this is usually the “requirements” –Issues in contemporary requirements Ambiguity Incompleteness Mistaking a solution for the problem –Analyze separate decisions separately 7INFO630 Week 6

8. www.ischool.drexel.edu The Business Decision Making Process 8INFO630 Week 6

9. www.ischool.drexel.edu Define the Selection Criteria Selection criteria need to be –Unique –Sufficient –Meaningful –Discriminating 9INFO630 Week 6

10. www.ischool.drexel.edu Typical Selection Criteria Financial –Initial investment –Present worth (Net present value) –Internal rate of return –Discounted payback period –… Technical –Performance –Reliability –Maintainability –Compatibility –… Non-technical –Reputable provider –Creature comfort –… 10INFO630 Week 6

11. www.ischool.drexel.edu The Business Decision Making Process 11INFO630 Week 6

12. www.ischool.drexel.edu Identify Reasonable Technically-feasible Solutions We’re usually pretty good at this… –Creative/lateral thinking helps (see [DeBono92] or [vonOech98]) 12INFO630 Week 6

13. www.ischool.drexel.edu The Business Decision Making Process 13INFO630 Week 6

14. www.ischool.drexel.edu Evaluate Each Proposal Against the Selection Criteria Proposals Financial Risk Morale Extend $66,021 0.40 1.00 Fix defects $58,056 0.20 0.50 Client-server $76,605 0.50 0.80 14INFO630 Week 6

15. www.ischool.drexel.edu The Business Decision Making Process 15INFO630 Week 6

16. www.ischool.drexel.edu Select the Preferred Proposal Comparing proposal from a financial perspective main topic of course More detail to follow –For-Profit: Ch 10-17 –Non-Profit: Ch 18 16INFO630 Week 6

17. www.ischool.drexel.edu The Business Decision Making Process 17INFO630 Week 6

18. www.ischool.drexel.edu Monitor the Performance of the Selected Proposal Quality of decision based on “estimation” –Bad estimate -> Bad decisions –Close the loop compare original to actual Improve estimation technique 18INFO630 Week 6

19. www.ischool.drexel.edu Monitor the Performance of the Selected Proposal Refine your estimation technique –Look at where you’ve been Have you been meeting expectations? Cash-flow stream matching actual cash flow? If out of “sync” with reality, switch? –Look at where you are Earned value –Ratio of estimated effort and schedule for WBS tasks already completed to the actual effort and schedule for the same tasks –Look at where you’re going Improve future estimates Common mistake –Resources available 100% to project 19INFO630 Week 6

20. www.ischool.drexel.edu Key Points There is a systematic process for making business decisions The process applies at many scales The process is more fluid than implied here 20INFO630 Week 6

21. www.ischool.drexel.edu Interest: The Time Value of Money Slides adapted from Steve Tockey – Return on Software 21INFO630 Week 6

22. www.ischool.drexel.edu Time is money Time value is quantifiable: interest Naming conventions in interest formulas Simple interest Compound interest Compound interest formulas –Using interest tables Selecting an interest formula Interest: Time-Value of Money Outline 22INFO630 Week 6

23. www.ischool.drexel.edu Time is Money Fundamental concept in business –A given amount of money at one time doesn’t have the same value as the same amount of money at a different time –In other words Its value changes over time 23INFO630 Week 6

24. www.ischool.drexel.edu An Experiment Give one person $10 now Promise to give another person $10 later Questions: –Who is better off, and why? –How much better off are they? –Would the $10 later person be willing to give up some in order to get it now? –Would the $10 now person be willing to wait if we promised to give them more later? 24INFO630 Week 6

25. www.ischool.drexel.edu Time Value is Quantifiable Interest –Money someone pays to use someone else’s money –Literally, a rental fee for money Evidence as early as 2000 BC Interest rate –Specifies the rental fee as a percent of the amount loaned, e.g., 6.825% Assumed to be annual unless noted 25INFO630 Week 6

26. www.ischool.drexel.edu Interest Rate What makes up an interest rate? 26INFO630 Week 6

27. www.ischool.drexel.edu The Lender’s Perspective Probability the borrower won’t repay –$3 default per $100 loaned  3% Cost of setting up and administering –$2 per $100 loaned  2% Compensation for loss of use of their own money –4.5% Probability prevailing interest rate will change –0.5% This lender should ask for 10% interest rate 27INFO630 Week 6

28. www.ischool.drexel.edu The Borrower’s Perspective Personal use –E.g. vacation, new car, house, … –How much is borrower willing to pay for satisfaction now rather than later? Business use –E.g., expand office space, fund new product development, buy new equipment, … –Expected return should be higher than loan interest rate 28INFO630 Week 6

29. www.ischool.drexel.edu Interest Rate In general, –Interest is thought of as a return that can be gained from productive investment of money Will investigate different formulas of “interest” –There are a set of standard formulas that allow you to convert the value of money at one point in time to the value of a different amount of money at some other time. First –Terms used 29INFO630 Week 6

30. www.ischool.drexel.edu Naming Conventions in Interest Formulas P –“Principal Amount”—how much is the money worth right now? –Also known as “present value” or “present worth” F –“Final Amount”—how much will the money be worth at a later time? –Also known as the “future value” or “future worth” i –Interest rate per period –Assumed to be an annual rate unless stated otherwise n –Number of interest periods between the two points in time A –“Annuity”—a stream of recurring, equal payments that would be due at the end of each interest period 30INFO630 Week 6 These are critical concepts!!!

31. www.ischool.drexel.edu Simple Interest Interest is directly proportional to P, n, i Borrowing $15k at 8% for 5 years –I = $15k x 5 x 0.08 = $6k –F = P + I = $15k + 6k = $21k 0 123n-1n known unknown 31INFO630 Week 6

32. www.ischool.drexel.edu Compound Interest Simple interest favors the borrower –Lender wants to consider unpaid, accrued interest as part of the loan (compound interest) Literally, lender wants to get interest on interest –Hence simple interest is not used often Borrowing $15k at 8% for 5 years –Borrower owes $15.0k + $1.2k = $16.2k after 1 st year –Borrower owes $16.2k + $1.3k = $17.5k after 2 nd year –Borrower owes $17.5k + $1.4k = $18.9k after 3 rd year –Borrower owes $18.9k + $1.5k = $20.4k after 4 th year –Borrower owes $20.4k + $1.6k = $22.0k after 5 th year –Compare this to simple interest case 32INFO630 Week 6

33. www.ischool.drexel.edu Compound Interest (cont) 33INFO630 Week 6

34. www.ischool.drexel.edu Compound Interest Formulas Six different compound interest formulas –Single-payment compound-amount (F/P) –Single-payment present-worth (P/F) –Equal-payment-series compound-amount (F/A) –Equal-payment-series sinking-fund (A/F) –Equal-payment-series capital-recovery (A/P) –Equal-payment-series present-worth (P/A) 34INFO630 Week 6

35. www.ischool.drexel.edu Single-Payment Compound-Amount (F/P) Most straight forward of the six compound interest formulas –Single payment at the end of a loan –Includes all of the compounded interest –Calculates unknown future value of some know present value (F given P) Generic cash-flow diagram – no payments during the loan! Example –How much will be owed if you borrow $15k at 8% for 5 years? 0 123n-1n known unknown 35INFO630 Week 6

36. www.ischool.drexel.edu Single-Payment Compound-Amount (F/P) Deriving the formula Year Owed at start Interest accrued Owed at end of year 1 P Pi P + Pi = P(1+i) 2 P(1+i) P(1+i)i P(1+i) + P(1+i)i = P(1+i) 3 P(1+i) P(1+i) i P(1+i) + P(1+i) i = P(1+i) n P(1+i) P(1+i) i P(1+i) + P(1+i) i = P(1+i) n-1n 1 2 2 2 223 36INFO630 Week 6

37. www.ischool.drexel.edu Single-Payment Compound-Amount (F/P) Formula Solving the sample problem –How much will be owed if you borrow $15k at 8% for 5 years? Shorthand notation F/P, i, n F = P ( ) F/P, 8%, 5 F = $15k ( ) 37INFO630 Week 6

38. www.ischool.drexel.edu How much will be owed if you borrow $15k at 8% for 5 years? YearOwed at startInterest accruedOwed at end of year 1$15K$15K *.08 = 1.2K$16.2K 2 $16.2K *.08 = 1.3K$17.5 K 3 $17.5 K *.08 = 1.4K$18.9 K 4 $18.9 K *.08 = 1.5K$20.4 K 5 $20.4 K *.08 = 1.6K$22 K

39. www.ischool.drexel.edu Interest Tables – Conversion Factor (Page 498) Table B-12 8% Interest Factors for Discrete Compounding Single-Payment Equal-Payment-Series Compound- Present- Compound- Sinking- Present- Capital- Amount Worth Amount Fund Worth Recovery Find F Given P Find P Given F Find F Given A Find A Given F Find P Given A Find A Given P n (F/P,i,n) (P/F,i,n) (F/A,i,n) (A/F,i,n) (P/A,i,n) (A/P,i,n) 11.0800 0.9259 1.0000 1.0000 0.9259 1.0800 21.1664 0.8573 2.0800 0.4808 1.7833 0.5608 31.2597 0.7938 3.2464 0.3080 2.5771 0.3880 41.3605 0.7350 4.5061 0.2219 3.3121 0.3019 51.4693 0.6806 5.8666 0.1705 3.9927 0.2505 61.5869 0.6302 7.3359 0.1363 4.6229 0.2163 71.7138 0.5835 8.9228 0.1121 5.2064 0.1921 81.8509 0.5403 10.6366 0.0940 5.7466 0.1740 91.9990 0.5002 12.4876 0.0801 6.2469 0.1601 102.1589 0.4632 14.4866 0.0690 6.7101 0.1490 So F/P, 8%, 5 F = $15k ( ) = $15K (1.4693) = $22.0395 39INFO630 Week 6

40. www.ischool.drexel.edu Single-Payment Present-Worth (P/F) P given F (P/F) –Calculates the unknown present value needed to return a future value Generic cash-flow diagram Example –How much would need to be deposited at 8% to end up with $15k after 5 years? 0 123n-1n unknown known 40INFO630 Week 6

41. www.ischool.drexel.edu Single-Payment Present-Worth (P/F) Deriving the formula –Rearrange the Single-payment Compound- Amount formula… –… to solve for P 41INFO630 Week 6

42. www.ischool.drexel.edu Single-Payment Present-Worth (P/F) Formula Solving the sample problem –How much would need to be deposited at 8% to end up with $15k after 5 years? Shorthand notation P/F, i, n P = F ( ) P/F, 8%, 5 P = $15k ( ) 42INFO630 Week 6

43. www.ischool.drexel.edu Interest Tables – Conversion Factor (Page 498) Table B-12 8% Interest Factors for Discrete Compounding Single-Payment Equal-Payment-Series Compound- Present- Compound- Sinking- Present- Capital- Amount Worth Amount Fund Worth Recovery Find F Given P Find P Given F Find F Given A Find A Given F Find P Given A Find A Given P n (F/P,i,n) (P/F,i,n) (F/A,i,n) (A/F,i,n) (P/A,i,n) (A/P,i,n) 11.0800 0.9259 1.0000 1.0000 0.9259 1.0800 21.1664 0.8573 2.0800 0.4808 1.7833 0.5608 31.2597 0.7938 3.2464 0.3080 2.5771 0.3880 41.3605 0.7350 4.5061 0.2219 3.3121 0.3019 51.4693 0.6806 5.8666 0.1705 3.9927 0.2505 61.5869 0.6302 7.3359 0.1363 4.6229 0.2163 71.7138 0.5835 8.9228 0.1121 5.2064 0.1921 81.8509 0.5403 10.6366 0.0940 5.7466 0.1740 91.9990 0.5002 12.4876 0.0801 6.2469 0.1601 102.1589 0.4632 14.4866 0.0690 6.7101 0.1490 So= $15K (.6806) = $10.209K P/F, 8%, 5 P = $15k ( ) 43INFO630 Week 6

44. www.ischool.drexel.edu Equal-Payment-Series Compound-Amount (F/A) F given A (F/A) –How much end up with based on series of equal payments made over time Retirement account Generic cash-flow diagram Example –How much would you end up with if you invested $1k at 8% at the end of each of the next 5 years? 012 3n-1 n known unknown 44INFO630 Week 6

45. www.ischool.drexel.edu Equal-Payment-Series Compound-Amount (F/A) Deriving the formula Multiply by (1+i) Subtract the first equation from the second Solve for F F = A(1) + A(1+i) + … + A(1+i) + A(1+i) n-2 n-1 F(1+i) = A(1+i) + A(1+i) + … + A(1+i) + A(1+i) n-1n F(1+i) = A(1+i) + A(1+i) + … + A(1+i) + A(1+i) n-1 2 n -F = -A - A(1+i) - A(1+i) - … - A(1+i) 2n-1 F(1+i) - F = -A + A(1+i) n Note: A1 = last payment – has no interest A(1+i) is the 2 nd to last payment, has interest 45INFO630 Week 6

46. www.ischool.drexel.edu Equal-Payment-Series Compound-Amount (F/A) Formula Solving the sample problem –How much would you end up with if you invested $1k at 8% at the end of each of the next 5 years? Shorthand notation F/A, i, n F = A ( ) F/A, 8%, 5 F = $1k ( ) 46INFO630 Week 6

47. www.ischool.drexel.edu Table B-12 8% Interest Factors for Discrete Compounding Single-Payment Equal-Payment-Series Compound- Present- Compound- Sinking- Present- Capital- Amount Worth Amount Fund Worth Recovery Find F Given P Find P Given F Find F Given A Find A Given F Find P Given A Find A Given P n (F/P,i,n) (P/F,i,n) (F/A,i,n) (A/F,i,n) (P/A,i,n) (A/P,i,n) 11.0800 0.9259 1.0000 1.0000 0.9259 1.0800 21.1664 0.8573 2.0800 0.4808 1.7833 0.5608 31.2597 0.7938 3.2464 0.3080 2.5771 0.3880 41.3605 0.7350 4.5061 0.2219 3.3121 0.3019 51.4693 0.6806 5.8666 0.1705 3.9927 0.2505 61.5869 0.6302 7.3359 0.1363 4.6229 0.2163 71.7138 0.5835 8.9228 0.1121 5.2064 0.1921 81.8509 0.5403 10.6366 0.0940 5.7466 0.1740 91.9990 0.5002 12.4876 0.0801 6.2469 0.1601 102.1589 0.4632 14.4866 0.0690 6.7101 0.1490 Interest Tables – Conversion Factor (Page 498) So= $1K (5.8666) = $5.8666K F/A, 8%, 5 F = $1k ( ) 47INFO630 Week 6

48. www.ischool.drexel.edu Equal-Payment-Series Sinking-Fund (A/F) A given F (A/F) –How much you want to end with, and you are trying to figure out how much to deposit each time Generic cash-flow diagram Example –How much would need to be invested at 8% at the end of each of the next 5 years to finish with $5k? 012 3n-1 n unknown known 48INFO630 Week 6

49. www.ischool.drexel.edu Equal-Payment-Series Sinking-Fund (A/F) Deriving the formula –Rearrange the Equal-payment-series Compound-Amount formula… –… to solve for A 49INFO630 Week 6

50. www.ischool.drexel.edu Equal-Payment-Series Sinking-Fund (A/F) Formula Solving the sample problem –How much would need to be invested at 8% at the end of each of the next 5 years to finish with $5k? Shorthand notation A/F, i, n A = F ( ) A/F, 8%, 5 A = $5k ( ) 50INFO630 Week 6

51. www.ischool.drexel.edu Table B-12 8% Interest Factors for Discrete Compounding Single-Payment Equal-Payment-Series Compound- Present- Compound- Sinking- Present- Capital- Amount Worth Amount Fund Worth Recovery Find F Given P Find P Given F Find F Given A Find A Given F Find P Given A Find A Given P n (F/P,i,n) (P/F,i,n) (F/A,i,n) (A/F,i,n) (P/A,i,n) (A/P,i,n) 11.0800 0.9259 1.0000 1.0000 0.9259 1.0800 21.1664 0.8573 2.0800 0.4808 1.7833 0.5608 31.2597 0.7938 3.2464 0.3080 2.5771 0.3880 41.3605 0.7350 4.5061 0.2219 3.3121 0.3019 51.4693 0.6806 5.8666 0.1705 3.9927 0.2505 61.5869 0.6302 7.3359 0.1363 4.6229 0.2163 71.7138 0.5835 8.9228 0.1121 5.2064 0.1921 81.8509 0.5403 10.6366 0.0940 5.7466 0.1740 91.9990 0.5002 12.4876 0.0801 6.2469 0.1601 102.1589 0.4632 14.4866 0.0690 6.7101 0.1490 Interest Tables – Conversion Factor (Page 498) So= $5K (0.1705) = $852.50 A/F, 8%, 5 A = $5k ( ) 51INFO630 Week 6

52. www.ischool.drexel.edu Equal-Payment-Series Capital-Recovery (A/P) A given P (A/P) –Standard formula for loan payments –Amount borrowed today. How much of an equal payment over the next N periods, will reduce the amount to zero at last payment. Generic cash-flow diagram Example –If you borrowed $25k at 7% for 5 years, what would your annual payments be? 0 123n-1n known unknown 52INFO630 Week 6

53. www.ischool.drexel.edu Equal-Payment-Series Capital-Recovery (A/P) Deriving the formula Start with Equal-payment-series Sinking-fund and Single-payment Compound-amount Substitute for F Simplify 53INFO630 Week 6

54. www.ischool.drexel.edu Equal-Payment-Series Capital-Recovery (A/P) Formula Solving the sample problem –If you borrowed $25k at 7% for 5 years, what would your annual payments be? Shorthand notation A/P, i, n A = P ( ) A/P, 7%, 5 A = $25k ( ) 54INFO630 Week 6

55. www.ischool.drexel.edu Equal-Payment-Series Present-Worth (P/A) P given A (P/A) –How much money today would be equivalent to future series of equal payments made over N periods at some interest rate? Generic cash-flow diagram Example –How much would need to be deposited today at 7% to give 10 end-of-year payments of $100 each, leaving $0 after the last payment? 0 123n-1nunknown known 55INFO630 Week 6

56. www.ischool.drexel.edu Equal-Payment-Series Present-Worth (P/A) Deriving the formula –Rearrange the Equal-payment-series Capital- recovery formula… –… to solve for P 56INFO630 Week 6

57. www.ischool.drexel.edu Equal-Payment-Series Present-Worth (P/A) Formula Solving the sample problem –How much would need to be deposited today at 7% to give 10 end-of- year payments of $100 each, leaving $0 after the last payment? Shorthand notation P/A, i, n P = A ( ) P/A, 7%, 10 P = $100 ( ) 57INFO630 Week 6

58. www.ischool.drexel.edu Summarizing the Formulas Vary depending on whether you are calculating –Forward/Backward Forward from a known present into an unknown future Backward from a known, desired future into an unknown present situation –Single-Payment/Equal Payment See next slide for help 58INFO630 Week 6

59. www.ischool.drexel.edu Selecting an Interest Formula 59INFO630 Week 6

60. www.ischool.drexel.edu Looks messy? The quantities ‘i’ and ‘n’ are usually given We’re solving for F, A, or P There are three pairs of formulas, connected by being the inverse of each other A/P = 1 / (P/A) F/P = 1 / (P/F) F/A = 1 / (A/F) INFO630 Week 660 Or ignore this slide if it’s confusing you.

61. www.ischool.drexel.edu Key Points “Amount of money” and “value” are different concepts –The same amount of money has different values at different times The time-value of money is quantified by interest Simple interest isn’t normally available Compound interest involves interest on interest –Several compound interest formulas exist (six) –Interest tables help solve compound interest calculations 61INFO630 Week 6

62. www.ischool.drexel.edu Other Interest Calculations Chapter 6 INFO630 Week 662

63. www.ischool.drexel.edu Toying with Chapter 5 This chapter introduces few new equations, but shows how you can work with the key six equations from chapter 5 Start by examining the interest rate, i We assumed it was known, and typically given for the rate it was compounded –6% annual interest, compounded annually –1.2% monthly interest, compounded monthly INFO630 Week 663

64. www.ischool.drexel.edu Different interest period and compounding frequencies What if that isn’t true? Convert the nominal interest rate (r) to the effective annual interest rate (i) i = (1 + r/m)^m -1 –Where ‘m’ is the number of compounding periods per year (see Table 6.1, p. 75, and fix m=365 for daily) and ^ is ‘to the power of’ INFO630 Week 664

65. www.ischool.drexel.edu Different interest period and compounding frequencies So 16% annual interest compounded quarterly (m=4) is really i = (1 + 0.16/4)^4 – 1 = 0.16985856 = 16.99% effective annual interest Or flip the equation around to solve for r r = m( (1+i)^(1/m) – 1) So 6.5% effective interest converted to monthly is r = 12( (1.065)^(1/12)-1)=6.31% INFO630 Week 665

66. www.ischool.drexel.edu Or even more arbitrary Or convert a nominal annual rate (r) based on one compounding period to any other compounding period (m) with i = (1 + r/m)^c – 1 where ‘c’ is the number of compounding periods in ‘i’ divided by the periods in ‘r’ –So 4% interest every 26 weeks compounded weekly, converts to quarterly (13 weeks) as i = (1+0.04/26)^13 – 1 = 2.02% INFO630 Week 666

67. www.ischool.drexel.edu APR APR (Annual Percentage Rate) shows up in ads all the time – it’s the nominal annual interest rate, but can be based on any period or compounding rate –Use the r formula on slide 65 to convert to the nominal annual rate (APR=r) –APR isn’t the effective annual percentage rate, since compounding can be not annual INFO630 Week 667

68. www.ischool.drexel.edu Cash flow rate versus compounding interval When the cash flow comes in faster or slower than the compounding of interest, or even at the same rate, use the formula on slide 64 to get the actual interest rate per compounding interval Then use the equations from chapter 5 with that value of ‘i’ INFO630 Week 668

69. www.ischool.drexel.edu Continuous compounding There is such a thing as continuous compounding, which means interest is compounded every moment Formulas for F, A, and P involve exponential terms (page 81) This is rarely used in reality INFO630 Week 669

70. www.ischool.drexel.edu Other special uses of Chapter 5 Many of the other examples are just working backward to solve for ‘i’ –Can interpolate on the tables in Appendix B, or solve analytically For example, to pay off a loan early you need to solve for the loan’s present worth (P) when you’re ready to pay it off INFO630 Week 670

71. www.ischool.drexel.edu Loan interest Loan payments (At) pay off interest (It) and principal (Bt) (the ‘t’s should be subscripts) At = It + Bt It = A*(P/A, i, n-t+1)*i Bt = A – It where A is the loan payment amount ‘t’ is the t th payment against the loan INFO630 Week 671

72. www.ischool.drexel.edu Loan payoff early If you increase the loan payment by E, how much faster do you pay it off? We had P/A = (P/A, i, n-t+1) after ‘t’ payments Now find the number of payments ‘j’ for which P/(A+E) = (P/A, i, j) is true Again, interpolation is often needed INFO630 Week 672

73. www.ischool.drexel.edu Interpolation review Linear interpolation lets you find the intermediate value between table entries The example on page 83 needs to interpolate between 18 and 19% interest entries for the value of F/P: 18% F/P=3.759 Z% F/P=3.852 19% F/P=4.021 INFO630 Week 673

74. www.ischool.drexel.edu Interpolation To solve this, these ratios hold (Z-18)/(19-18) = (3.852-3.759)/(4.021-3.759) Solve for Z (Z-18)/1 = 0.093/0.262 = 0.35496 Z = 18 + 1*0.35496 = 18.355% INFO630 Week 674

75. www.ischool.drexel.edu Other tricks Notice that solving the problems in this chapter often involve converting the given interest rates into the effective annual rate Then apply the right F, A, or P formula to solve the problem Also note that interpolation is often helpful to solve for interest rates or remaining loan durations INFO630 Week 675

76. www.ischool.drexel.edu Other tricks In other real world situations, look out for sneaky deals where interest is calculated based on the total principal of the loan –The real or effective interest rate could be much higher than it seems, since you’re paying interest on principal which has already been paid off  INFO630 Week 676