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- 1. CHAPTER 4 Part ….2 The Time Value of Money Created ByEng. Maysa Faroon Gharaybeh
- 2. Relating a Uniform Series(Ordinary Annuity) To Presentand Future Equivalent Values
- 3. 1. Finding F given A:• Finding future equivalent income (inflow) value given a series of uniform equal Payments• F= (1i ) N 1 (4-8) A i – (1i ) 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. Example 4-7
- 5. See the next slide and get (F/A,6%,40)
- 6. Example 4-8
- 7. 2. Finding P given A:• Finding present equivalent value given a series of uniform equal receipts 1 i N 1• P = A N i1 i (4-10) 1 i N 1 uniform series present worth factor. – N i1 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. Example 4-9
- 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. 4. 4. Finding A given P: Finding A given P:• Finding amount A of a uniform series when given i1 i N A equivalent the P (4-14) 1 i 1 N i1 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. 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. Linear Interpolation6% 9.8975i’% 107% 10.2598
- 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. 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. Summary
- 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. 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. Equivalence Calculations Involving Multiple Interest Formulas
- 19. • End of Chapter 4 PART 2• See you next lecture with 4 PART 3• Don’t, miss it !!!!!

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