6
advanced-math

$50,000 in a retirement account earns 6% annually. Assuming no additional deposits, what will it be worth in 30 years?

A

$287,174.56

B

$200,000.00

C

$150,000.00

D

$300,000.00

Correct Answer: A

Choice A is the correct answer. Calculate long-term growth.

  1. Formula: A=50000(1.06)30A = 50000(1.06)^{30}.
  2. Calculate: (1.06)305.7435(1.06)^{30} \approx 5.7435, so A287,175A \approx 287,175.
  3. Rule of 72: Doubling time ≈ 726=12\frac{72}{6} = 12 years. In 30 years ≈ 2.5 doublings → 50k×22.5283k50k \times 2^{2.5} \approx 283k ✓.

💡 Strategic Tip: Long-term exponential growth can produce dramatic results.

Choice B is incorrect because this only quadruples the principal. Choice C is incorrect because this only triples the principal. Choice D is incorrect because the calculation doesn't match.