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

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