Example From Midterm 1

Year Benefit

0 1000

1 1000

2 1000

3 500

4 250

5 125

. .

. .

. .

9 7.8125

Interest rate i=10%

*Q1: what is the present worth of this asset?*

(a) 3,421.48

(b) 3,399.17

(c) 3,090.15

(d) 3,774.67

(e) None of the above.

This is an irregular series which consists of:

- A present worth P0=1000
- A future worth F1=1000 at period 1
- A geometric gradient series from period 2 to period 9 with A1=1000,g=-50%,N=8.The present worth of this series is at period 1 so it must be shifted to period 0 by dividing (1+10%)

The final result:

P=P0+F1/1.1+A1(P⁄A1,g=-0.5,i=0.1,8)/1.1

P=1000+1000/1.1+1000[(1-(1-0.5)^8 (1+0.1)^-8)/(0.1+0.5)]/1.1=3421.48

The right answer is (a)

*Q2:How could you represent the present worth of payments from period 2 through period
9 in factor notation?*

The right answer is A1(P⁄A1,g=-0.5,i=0.1,8)/1.1

page revision: 8, last edited: 21 Oct 2013 20:44