1. Model Three: An Investment Problem
By Evan Nixon

2. The problem We have been given $1.5 million to invest over three years
4 Different rates are available:
Our goal is to maximize the value of the investment over three years
Year 1
Year 2
Year 3
Investment A 7%
Investment B 5% 8%
Investment C
20 % (three years)
Investment D
N/A
16% (two years)

3. How to solve the problem
A simple tree exploring our different options can illustrate different outcomes
A complete tree will cover all scenarios and can show us which investment will be the most profitable

4. Beginning: $1,500,000
A: 7%
$1,605,000
A: 7% $1,717,350
A: 7% $1,837,565
B: 8% $1,854,738
B: 8% $1,733,400
A: 7% $1,854,738
B: 8% $1,872,072
D: 16% $1,861,800
B: 5% $1,575,000
A: 7% $1,685,250
A: 7% $1,803,218
B: 8% $1,820,070
B: 8% $1,701,000
A: 7% $1,820,070
B: 8% $1,837,080
D: 16% $1,827,000
C: 20% $1,800,000

5. Beginning: $1,500,000
A: 7%
$1,605,000
A: 7% $1,717,350
A: 7% $1,837,565
B: 8% $1,854,738
B: 8% $1,733,400
A: 7% $1,854,738
B: 8% $1,872,072
D: 16% $1,861,800
B: 5% $1,575,000
A: 7% $1,685,250
A: 7% $1,803,218
B: 8% $1,820,070
B: 8% $1,701,000
A: 7% $1,820,070
B: 8% $1,837,080
D: 16% $1,827,000
C: 20% $1,800,000

6. Beginning: $1,500,000
A: 7%
$1,605,000
A: 7% $1,717,350
A: 7% $1,837,565
B: 8% $1,854,738
B: 8% $1,733,400
A: 7% $1,854,738
B: 8% $1,872,072
D: 16% $1,861,800
B: 5% $1,575,000
A: 7% $1,685,250
A: 7% $1,803,218
B: 8% $1,820,070
B: 8% $1,701,000
A: 7% $1,820,070
B: 8% $1,837,080
D: 16% $1,827,000
C: 20% $1,800,000

7. The Solution
As seen in the outcome tree, the investment will make the most money if it is invested in A for year one and B for years two and three.
The investment will have a value of $1,872,072 after three years, a 24.8% increase from before
Year 1
Year 2
Year 3
Investment A 7%
Investment B 5% 8%
Investment C
20 % (three years)
Investment D
N/A
16% (two years)

8. Fin