Answer:
Goal: maximize return at the end of the fourth year.
Future value of each option:
First choise: $ 11,730,289.64
Second choise: $ 12,559,457.84
Conclusion:
It is better to pick the second option as yields a better return
Explanation:
We solve for the future value of the cashflow of each option:
First choise:
End of the first year:
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
Principal 2,000,000.00
time 36.00 (form end of the first to end of the fourth)
rate 0.00917 (11% / 12 months as it compounds monthly)
[tex]2000000 \: (1+ 0.00916666666666667)^{36} = Amount[/tex]
Amount $2,777,757.26
End of the second year:
Principal 2,000,000.00
time 24.00
rate 0.00917
[tex]2000000 \: (1+ 0.00916666666666667)^{24} = Amount[/tex]
Amount $2,489,657.04
End of the third year:
Principal 4,000,000.00
time 12.00
rate 0.00917
[tex]4000000 \: (1+ 0.00916666666666667)^{12} = Amount[/tex]
Amount $4,462,875.34
End of the fourth year: $2,000,000
Total:
$2,777,757.26
$2,489,657.04
$4,462,875.34
$2,000,000
$ 11,730,289.64
Second choise:
First year
Principal 1,000,000.00
time 36.00
rate 0.00917
[tex]1000000 \: (1+ 0.00916666666666667)^{36} = Amount[/tex]
Amount 1,388,878.63
Second year:
Principal 1,000,000.00
time 24.00
rate 0.00917
[tex]1000000 \: (1+ 0.00916666666666667)^{24} = Amount[/tex]
Amount 1,244,828.52
Third Year
Principal 8,000,000.00
time 12.00
rate 0.00917
[tex]8000000 \: (1+ 0.00916666666666667)^{12} = Amount[/tex]
Amount 8,925,750.69
Fourth year: 1,000,000
Total
1,388,878.63
1,244,828.52
8,925,750.69
1,000,000.00
12,559,457.84
