Answer:
net wortht -143,280.85
equivalent annual cost $ 24,932.98
Explanation:
We sovle for the present value of each annuity:
The first three years:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 31,000.00
time 3
rate 0.08
[tex]31000 \times \frac{1-(1+0.08)^{-3} }{0.08} = PV\\[/tex]
PV $79,890.0066
Then the second phase annuity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 20,000.00
time 5
rate 0.08
[tex]20000 \times \frac{1-(1+0.08)^{-5} }{0.08} = PV\\[/tex]
PV $79,854.2007
NOw, we discount this as it is three years into the future
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity $79,854.2007
time 3.00
rate 0.08000
[tex]\frac{79854.2007415617}{(1 + 0.08)^{3} } = PV[/tex]
PV 63,390.8391
Total net worth:
79,890.0066 - 63,390.8391 = -143,280.85
The EAC will be the annuity which makes the Present work
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV 143,280.85
rate 0.08
time 8
[tex]143280.85 \div \frac{1-(1+0.08)^{-8} }{0.08} = C\\[/tex]
C $ 24,932.983
