A price index rises from 100 to 121 over two years. What compound annual rate does this represent?
Correct Answer
C) 10.0 percent a year
Why this is correct: The index rose from 100 to 121, a 21% total increase over two years. This represents a 10% compound annual rate because 1.10 * 1.10 = 1.21. Simply dividing 21% by 2 years (10.5%) ignores compounding. Why the other choices are wrong: 21.0 percent a year would yield a much higher result. 10.5 percent a year is the simple average, not the compound rate. 12.1 percent a year does not mathematically result in 121 from 100 in two years. Exam tip: For compound growth, find the annual multiplier: (Ending Value / Starting Value)^(1/Number of Years) - 1.
Why This Is the Correct Answer
Why this is correct: The index rose from 100 to 121, a 21% total increase over two years. This represents a 10% compound annual rate because 1.10 * 1.10 = 1.21. Simply dividing 21% by 2 years (10.5%) ignores compounding. Why the other choices are wrong: 21.0 percent a year would yield a much higher result. 10.5 percent a year is the simple average, not the compound rate. 12.1 percent a year does not mathematically result in 121 from 100 in two years. Exam tip: For compound growth, find the annual multiplier: (Ending Value / Starting Value)^(1/Number of Years) - 1.
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