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Finance:

Stock A is initially worth [tex]\[tex]$1300[/tex] and loses [tex]\$[/tex]80[/tex] each month. Stock B is initially worth [tex]\$400[/tex] and gains [tex]9.5\%[/tex] each month. When will Stock B be worth more than Stock A?

Sagot :

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.