Answer:
The best financial option would be the second as his PV is the lowest
Explanation:
we will calcualte each option present value using the annuit formula
[tex]PTM \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
second option
PTM 82,000
time 10 years
rate 0.08
[tex]82000 \times \frac{1-(1+0.08)^{-10} }{0.08} = PV\\[/tex]
PV $550,226.6747 + 400,000 = 950,226
third option (annuity-due)
PTM 140,000
time 10years
rate 0.08
[tex]140000 \times \frac{1-(1+0.08)^{-10} }{0.08} (1+0.08)= PV\\[/tex]
PV $1,014,564.3075
fourth option (lump sum present value)
[tex]\frac{Nominal}{(1 + rate)^{time} } = PV[/tex]
Nominal: 1,610,000.00
time 5 years
rate 0.08
[tex]\frac{1610000}{(1 + 0.08)^{5} } = PV[/tex]
PV 1,095,738.95