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advanced-mathTwo investments:
- Investment P: $1,000 growing at 10% annually
- Investment Q: $800 growing at 15% annually
After many years, which will be worth more?
A
Investment Q
B
Investment P
C
They will be equal
D
Cannot determine
Correct Answer: A
Choice A is the correct answer. Compare growth factors over the long term.
- Investment P: .
- Investment Q: .
- Long-term: , so Q's base is larger.
- Conclusion: As , the larger base dominates, so Q eventually exceeds P.
💡 Strategic Tip: In exponential growth, larger base always wins in the long run.
Choice B is incorrect because despite higher initial value, lower growth rate loses. Choice C is incorrect because different bases mean they diverge. Choice D is incorrect because we can determine this from the growth rates.