9
advanced-math

Two 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.

  1. Investment P: P(t)=1000(1.10)tP(t) = 1000(1.10)^t.
  2. Investment Q: Q(t)=800(1.15)tQ(t) = 800(1.15)^t.
  3. Long-term: 1.15>1.101.15 > 1.10, so Q's base is larger.
  4. Conclusion: As tt \to \infty, 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.