This document discusses methods for calculating present and future values of uniform series (ordinary annuities) using time value of money formulas. It covers finding the future value given the payment amount, finding the present value given the payment amount, finding the payment amount given the future or present value, and methods for determining the number of periods. It also discusses deferred annuities and calculations involving multiple time value of money formulas.

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 !!!!!