Question

Calculate x that makes the present worth of the following cash flow at interest rate equals 10 % equals to $22222?

please in the fastest way and the easiest way

10000 2000 3000 4000 5000 X х X X 0 1 2 3 4 5 6 7 8

Answer 1

As per given condition

22222 = 10000 + x *((P/F,10%,1)+(P/F,10%,3)+(P/F,10%,5)+(P/F,10%,7)) + 2000*(P/F,10%,2) + 3000*(P/F,10%,4) + 4000*(P/F,10%,6) + 5000*(P/F,10%,8)

x *((P/F,10%,1)+(P/F,10%,3)+(P/F,10%,5)+(P/F,10%,7)) + 2000*(P/F,10%,2) + 3000*(P/F,10%,4) + 4000*(P/F,10%,6) + 5000*(P/F,10%,8) = 22222 - 10000

x *(0.909091 + 0.751315 + 0.620921 + 0.513158) + 2000*0.826446 + 3000*0.683013 + 4000*0.564474 + 5000*0.466507 = 12222

x*2.794485 = 12222 - 8292.36 = 3929.64

x = 3929.64 / 2.794485 = 1406.21