A property sold for $400,000 and resold three years later for $463,050 with no physical change. What compound annual rate does this indicate?
Correct Answer
A) 5.0 percent a year
Why this is correct: The original explanation shows the calculation: $400,000 * (1 + r)^3 = $463,050. Solve for r: (1+r)^3 = $463,050/$400,000 = 1.157625. The cube root of 1.157625 is 1.05, so r = 0.05 or 5%. The governing concept is compound annual growth rate (CAGR). Why the other choices are wrong: 5.3 percent a year might come from simple interest calculation: ($63,050 gain / 3 years) / $400,000 = 5.25%. 15.8 percent a year is the total appreciation over 3 years ($63,050/$400,000), not annualized. 4.2 percent a year is not supported by the math. Exam tip: For compound growth, use: (End Value / Start Value)^(1/n) - 1, where n is years.
Why This Is the Correct Answer
Why this is correct: The original explanation shows the calculation: $400,000 * (1 + r)^3 = $463,050. Solve for r: (1+r)^3 = $463,050/$400,000 = 1.157625. The cube root of 1.157625 is 1.05, so r = 0.05 or 5%. The governing concept is compound annual growth rate (CAGR). Why the other choices are wrong: 5.3 percent a year might come from simple interest calculation: ($63,050 gain / 3 years) / $400,000 = 5.25%. 15.8 percent a year is the total appreciation over 3 years ($63,050/$400,000), not annualized. 4.2 percent a year is not supported by the math. Exam tip: For compound growth, use: (End Value / Start Value)^(1/n) - 1, where n is years.
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