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A bank's CD pays 2% interest for the first year and 18% interest for the second year, each compounded annually on the running balance. A competing CD pays a single fixed annual rate r compounded annually for two years and produces the same final balance. Which is nearest to r?
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Correct answer
B
The two-year growth factor is 1.02 × 1.18 = 1.2036. The equivalent fixed rate satisfies (1 + r)² = 1.2036, so 1 + r = √1.2036 ≈ 1.09709, giving r ≈ 9.71%, distinctly below the arithmetic mean.
(C) 10.0% is the arithmetic average of 2% and 18%, the named false summit; the true equivalent is the geometric mean, which sits noticeably below it because squaring penalizes the spread between the two rates. (D) 14.0% over-weights the high year; (A) 2.0% and (E) 18.0% just echo a single year.
back-solving each choice means squaring (1 + r) and comparing to 1.2036, and only 9.7% lands there. the arithmetic-mean reflex overshoots by about 0.3 points.
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