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# economy Ch4part2_by louy Al hami

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Engineering Economy

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### economy Ch4part2_by louy Al hami

1. 1. CHAPTER 4 Part ….2 The Time Value of Money Created ByEng. Maysa Faroon Gharaybeh
2. 2. Relating a Uniform Series(Ordinary Annuity) To Presentand Future Equivalent Values
3. 3. 1. Finding F given A:• Finding future equivalent income (inflow) value given a series of uniform equal Payments• F=  (1i ) N 1 (4-8) A    i   –  (1i ) N 1 uniform series compound amount factor .    i   – functionally expressed as F = A ( F / A,i%,N ) – predetermined values are in column 4 of Appendix C of text F=? 0 1 2 3 4 5 6 7 8 A=
4. 4. Example 4-7
5. 5. See the next slide and get (F/A,6%,40)
6. 6. Example 4-8
7. 7. 2. Finding P given A:• Finding present equivalent value given a series of uniform equal receipts  1  i N  1• P = A N   i1  i   (4-10)  1  i N  1 uniform series present worth factor. –  N   i1  i   – functionally expressed as P = A ( P / A,i%,N ) – predetermined values are in column 5 of Appendix C of text A= 1 2 3 4 5 6 7 8 P=?
8. 8. Example 4-9
9. 9. 3. Finding A given F:• Finding amount A of a uniform series when given the equivalent future value  i  A  F   1  i   1   N  (4-12) –  i  sinking fund factor    1  i   1  N   – functionally expressed as A = F ( A / F,i%,N ) – predetermined values are in column 6 of Appendix C of text F= 1 2 3 4 5 6 7 8 A =?
10. 10. 4. 4. Finding A given P: Finding A given P:• Finding amount A of a uniform series when given  i1  i N  A  equivalent the P  (4-14)  1  i   1 N  i1  i N  –   capital recovery factor.  1  i   1 N – functionally expressed as A = P ( A / P,i%,N ) – predetermined values are in column 7 of Appendix C P= 0 1 2 3 4 5 6 7 8 A =?
11. 11. 5. Finding N when given A, P and i:• Finding #of periods when given present & annuity value at i% interest rate.• Using the relationship between P & A 6. Finding N when given A, F and i:• Finding #of periods when given Future & annuity value at i% interest rate.• Using the relationship between F & A
12. 12. Linear Interpolation6% 9.8975i’% 107% 10.2598
13. 13. Q 4-39 page 197 Q …. A 40-years old person wants to accumulate \$500,000 by age of 65. how much will she need to save each month , starting one month from now, if the interest rate is 0.5% per month ? Solution ….. (65-40 = 25 years) N = 12 month × 25 = 300 months A = F(A/F, 0.5%, 300)
14. 14. A = \$500,000 (A/F, 0.5%, 300) = \$500,000 =  0.005 A= \$500,000   1  0.005  1  300 (4-12)  A = \$720 per month
15. 15. Summary
16. 16. ‫•‬ ‫عش كل لحظة من حياتك كأنها آخر لحظة لك في الحياة‬ ‫عش بالحب و األمل .. عش بالكفاح و التسامح‬ ‫وقدر قيمــــــــة الحيــــــــــــــــــــــــــاة وتوكل على هللا‬‫د.ابراهيم الفقي‬
17. 17. Deferred Annuity • If an annuity is deferred j periods, where j < N And finding P given A for an ordinary annuity is expressed by: P = A ( P / A, i %, N ) • This is expressed for a deferred annuity by: A ( P / A, i%, N - j ) at end of period j • This is expressed for a deferred annuity by: P0 = A ( P / A, i%, N - j ) ( P / F, i%, j ) at time 0 (time present)
18. 18. Equivalence Calculations Involving Multiple Interest Formulas
19. 19. • End of Chapter 4 PART 2• See you next lecture with 4 PART 3• Don’t, miss it !!!!!