To determine when Stock B will be worth more than Stock A, follow these steps:
1. Initialize the values for both stocks:
- Stock A starts at \[tex]$1300.
- Stock B starts at \$[/tex]400.
2. Define the rate of change for each stock:
- Stock A loses \[tex]$80 each month.
- Stock B gains 9.5% of its current value each month.
3. Track the values month by month until Stock B exceeds Stock A:
- Month 0:
- Stock A: \$[/tex]1300
- Stock B: \[tex]$400
- Month 1:
- Stock A: \$[/tex]1300 - \[tex]$80 = \$[/tex]1220
- Stock B: \[tex]$400 + (9.5% of \$[/tex]400) = \[tex]$400 + \$[/tex]38 = \[tex]$438
- Month 2:
- Stock A: \$[/tex]1220 - \[tex]$80 = \$[/tex]1140
- Stock B: \[tex]$438 + (9.5% of \$[/tex]438) ≈ \[tex]$438 + \$[/tex]41.61 ≈ \[tex]$479.61
- Month 3:
- Stock A: \$[/tex]1140 - \[tex]$80 = \$[/tex]1060
- Stock B: \[tex]$479.61 + (9.5% of \$[/tex]479.61) ≈ \[tex]$479.61 + \$[/tex]45.56 ≈ \[tex]$525.17
- Month 4:
- Stock A: \$[/tex]1060 - \[tex]$80 = \$[/tex]980
- Stock B: \[tex]$525.17 + (9.5% of \$[/tex]525.17) ≈ \[tex]$525.17 + \$[/tex]49.89 ≈ \[tex]$575.06
- Month 5:
- Stock A: \$[/tex]980 - \[tex]$80 = \$[/tex]900
- Stock B: \[tex]$575.06 + (9.5% of \$[/tex]575.06) ≈ \[tex]$575.06 + \$[/tex]54.63 ≈ \[tex]$629.69
- Month 6:
- Stock A: \$[/tex]900 - \[tex]$80 = \$[/tex]820
- Stock B: \[tex]$629.69 + (9.5% of \$[/tex]629.69) ≈ \[tex]$629.69 + \$[/tex]59.82 ≈ \[tex]$689.51
- Month 7:
- Stock A: \$[/tex]820 - \[tex]$80 = \$[/tex]740
- Stock B: \[tex]$689.51 + (9.5% of \$[/tex]689.51) ≈ \[tex]$689.51 + \$[/tex]65.51 ≈ \[tex]$755.02
Since at Month 7, Stock B (\$[/tex]755.02) is greater than Stock A (\[tex]$740), Stock B surpasses Stock A in value during the seventh month.
Conclusion:
Stock B will be worth more than Stock A after 7 months. At that time, Stock A will be worth \$[/tex]740, and Stock B will be worth approximately \$755.02.
