GRE General TestQuantitative ReasoningHard
A city planner is evaluating population growth. The population of a town is currently 15,000. If it grows at an annual rate of 2% compounded annually, what will be the approximate population after 5 years?
- A17,300
- B16,530
- C16,561
- D16,800
Show answer & explanationAnswer & explanation
Correct answer: C. 16,561
This is a compound interest problem. The formula for compound growth is P = P0 * (1 + r)^n, where P0 is the initial population, r is the annual growth rate, and n is the number of years. P = 15,000 * (1 + 0.02)^5 = 15,000 * (1.02)^5. Calculating (1.02)^5 ≈ 1.10408. So, P ≈ 15,000 * 1.10408 = 16,561.2. Rounded to the nearest whole number, it is 16,561.
Why the other options are wrong
- A. This is an overestimation, possibly from incorrect compounding or rounding.
- B. This is likely a miscalculation of the exponent or rounding error.
- D. This might be a simple interest calculation (15000 * (1 + 0.02*5)) which is incorrect for compounded growth.
Compound Annual Growth
Compound annual growth refers to the growth of a quantity over time, where the growth rate is applied to the accumulated amount from previous periods, leading to exponential increase.
- Formula: Future Value = Present Value * (1 + Rate)^Periods.
- The 'rate' must be annual if 'periods' are years.
- Differs from simple interest, which only applies to the initial principal.
Memory trick: Compounding grows like a snowball, adding more to its own mass.