Engineering Economy

1. CHAPTER 4
Part ….2
The Time Value of Money
Created By
Eng. Maysa Faroon Gharaybeh

2. Relating a Uniform Series
(Ordinary Annuity) To Present
and Future Equivalent Values

5. 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=

6. Example 4-7

7. See the next slide and get (F/A,6%,40)

9. Example 4-8

10. 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=?

11. Example 4-9

15. 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 =?

16. 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 =?

19. 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

24. Linear Interpolation
6% 9.8975
i’% 10
7% 10.2598

25. 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)

26. 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

27. Summary

29. ‫•‬
‫عش كل لحظة من حياتك كأنها آخر لحظة لك في الحياة‬
‫عش بالحب و األمل .. عش بالكفاح و التسامح‬
‫وقدر قيمــــــــة الحيــــــــــــــــــــــــــاة وتوكل على هللا‬
‫د.ابراهيم الفقي‬

30. 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)

34. Equivalence Calculations Involving
Multiple Interest Formulas

39. • End of Chapter 4 PART 2
• See you next lecture with 4 PART 3
• Don’t, miss it !!!!!