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

An investor buys a zero-coupon bond for 7,440 that pays 10,000 in exactly 5 years. The annualized implied rate of return, using annual compounding, is closest to:

The implied annual return is about 6.1%. Solve (10,000/7,440)^(1/5) − 1, which gives roughly 6.1%. Simply dividing the 34.4% total gain by five years ignores compounding and overstates the rate.

  1. A5.0%
  2. B6.1%Correct
  3. C7.5%

Explanation

Implied rate = (10,000/7,440)^(1/5) − 1 = (1.34409)^(0.2) − 1. ln(1.34409)=0.29582; divided by 5 = 0.059164; exp = 1.06095, so about 6.1%. Dividing the total gain of 34.4% by 5 gives 6.9%, which ignores compounding. A 5.0% rate would give a price of 7,835.

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