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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 from the actual CD is 1.02 × 1.18 = 1.2036. The equivalent fixed rate r must satisfy (1 + r)² = 1.2036, so 1 + r = √1.2036 ≈ 1.0971, giving r ≈ 9.7%, distinctly below the arithmetic mean of the two rates.
Back-solving each choice means squaring (1 + r) and comparing it to 1.2036, and only 9.7% lands there. The arithmetic-mean reflex overshoots the true value by about 0.3 percentage points because squaring a rate penalizes a wide spread between the two years more than a simple average captures.
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