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CFA Level I · CFA Level I Exam · The Time Value of Money in Finance

An investment grows from 50,000 to 80,000 over 4 years with interest compounded quarterly. The stated annual rate is closest to:

The stated annual rate is about 11.9%. With 16 quarters, the quarterly rate is 1.6^(1/16) − 1, roughly 2.98%. Multiplying by four gives the stated rate near 11.9%; the effective annual rate would be higher at about 12.5%.

  1. A11.8%
  2. B11.9%Correct
  3. C12.0%

Explanation

There are 16 quarters. Periodic rate = (80,000/50,000)^(1/16) − 1 = 1.6^(0.0625) − 1. ln1.6=0.470004; /16=0.029375; exp=1.029811, so 2.9811% per quarter. Stated annual rate = 4 × 2.9811% = 11.92%, about 11.9%. The effective annual rate is 12.0%×? (1.029811^4−1 = 12.47%), a different measure, so it is not the stated rate.

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