Answer:
The best would be the first option of a single payment of 64,000
As the discounted value of the other option is lower
FV of the apayment $1,318,079.4942
Explanation:
(1) PV 64,000
(2) 20,000 + PV of the annuity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 8,000.00
time 6
rate 0.06
[tex]8000 \times \frac{1-(1+0.06)^{-6} }{0.06} = PV\\[/tex]
PV $39,338.59
39,338.59 + 20,000 = 59,338.59
(3) PV of the annuity
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 13,000.00
time 6
rate 0.06
[tex]13000 \times \frac{1-(1+0.06)^{-6} }{0.06} = PV\\[/tex]
PV $63,925.2162
second question:
future value of annuity
[tex]C \times \frac{(1+r)^{time} -1}{rate} = FV\\[/tex]
C 100,000.00
time 10
rate 0.06
[tex]100000 \times \frac{(1+0.06)^{10} -1}{0.06} = FV\\[/tex]
PV $1,318,079.4942
