This document shows the present worth of a cash flow using factor notation. The cash flow has no payments for the first two years, then payments of $1 to $15 from years 3 to 10. The solution expresses the present worth of each payment as the cash amount divided by the appropriate present worth factor of (1+i)^n, where i is the interest rate and n is the year of the cash flow.

1. Show, in factor notation, the present worth of the following cash flow.
Year Cash
0 0
1 0
2 0
3 1
4 3
5 5
6 7
7 9
8 11
9 13
10 15
Solution
Year
Factor Name Factor Notation Formula
Present Worth Factor = ( P/F, i,N) = F/(1+i)^N
Year Cash Present Worth
0 0 0
1 0 0
2 0 0
3 1 =1/(1+i)^3
4 3 =3/(1+i)^4
5 5 =5/(1+i)^5

2. 6 7 =7/(1+i)^6
7 9 =9/(1+i)^7
8 11 =11/(1+i)^8
9 13 =13/(1+i)^9
10 15 =15/(1+i)^10