Find the value of x that makes the equivalent annual worth in years 1 through 8

Question

Find the value of x that makes the equivalent annual worth in years 1 through 8 equal to $700 per year. Use an interest rate of 12% per year. The cash flow in year 0 and year 8 has an unknown value x and 1 through 7 has an annual worth of $700 Find the value of x that makes the equivalent annual worth in years 1 through 8 equal to $700 per year. Use an interest rate of 12% per year. The cash flow in year 0 and year 8 has an unknown value x and 1 through 7 has an annual worth of $700 Find the value of x that makes the equivalent annual worth in years 1 through 8 equal to $700 per year. Use an interest rate of 12% per year. The cash flow in year 0 and year 8 has an unknown value x and 1 through 7 has an annual worth of $700

Explanation / Answer

Answer
the present value of the cash flow from 1 to 8 with x
Formula:
P=A*(P|A,i,n) +x+x*(1+i)^(-n)
P=present value
i=interest rate
n=years
A=annual uniform value

P=700*(P|A,12%,7)+x+x*(1.12^(-8))
=700*4.564+x(1+(1.12^(-8)))
=3194.8+X*1.40388323
and PV of the cash flow from 1 to 8
P=A*(P|A,i,n)
=700*(P|A,12%,8)
=700*4.968
=3477.6

equating both the equations
3194.8+x*1.40388323=3477.6
x=282.8/1.40388323
=201.441255
The value of x is $201.44

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