CHAPTER 4 Part ….2

The Time Value of Money

Created By

Eng. Maysa Faroon Gharaybeh

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

1. Finding F given A: • Finding future equivalent income (inflow) value given a

series of uniform equal Payments • F = (4-8)

– uniform series compound amount factor

. – functionally expressed as F = A ( F / A,i%,N ) – predetermined values are in column 4 of Appendix C

of text

F = ?

1 2 3 4 5 6 7 8 A = 0

i

NiA

1)1(

i

Ni 1)1(

Example 4-7

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

Example 4-8

2. Finding P given A:

• Finding present equivalent value given a series of

uniform equal receipts

• P = (4-10)

– uniform series present worth factor.

– functionally expressed as P = A ( P / A,i%,N )

– predetermined values are in column 5 of Appendix

C of text

P = ?

1 2 3 4 5 6 7 8 A =

N

N

ii

iA

1

11

N

N

ii

i

1

11

Example 4-9

3. Finding A given F:

• Finding amount A of a uniform series when given the

equivalent future value

(4-12)

– sinking fund factor

– 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 =?

11N

i

iFA

11N

i

i

4. 4. Finding A given P: Finding A given P:

• Finding amount A of a uniform series when given

the equivalent (4-14)

– capital recovery factor.

– functionally expressed as A = P ( A / P,i%,N )

– predetermined values are in column 7 of

Appendix C P =

1 2 3 4 5 6 7 8 A =? 0

11

1N

N

i

iiPA

11

1N

N

i

ii

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

6% 9.8975

i’% 10

7% 10.2598

Linear Interpolation

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)

A = $500,000 (A/F, 0.5%, 300) = $500,000 =

A = (4-12)

A = $720 per month

1005.01

005.0000,500$

300

Summary

•

عش كل لحظة من حياتك كأنها آخر لحظة لك في الحياة

عش بالكفاح و التسامح.. عش بالحب و األمل

وقدر قيمــــــــة الحيــــــــــــــــــــــــــاة وتوكل على هللاابراهيم الفقي .د

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)

Equivalence Calculations Involving Multiple Interest Formulas

• End of Chapter 4 PART 2

• See you next lecture with 4 PART 3

• Don’t, miss it !!!!!