You have just purchased a 7-year zero-coupon bond with a yield to maturity of 11% and a par value of $1,000. What would your rate of return at the end of the year be if you sell the bond? Assume the yield to maturity on the bond is 9% at the time you sell.

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Quizplus · Accepted Answer

The rate of return can be calculated by first finding the purchase price of the bond using the initial yield to maturity (11%), and then finding the selling price using the new yield to maturity (9%). The purchase price (P) of a zero-coupon bond is calculated using the formula P = F / (1 + r)^n, where F is the face value, r is the yield to maturity, and n is the number of years until maturity. For the purchase price, P = $1,000 / (1 + 0.11)^7 ≈ $513.16. For the selling price one year later, with 6 years remaining until maturity and a new yield of 9%, the price would be P = $1,000 / (1 + 0.09)^6 ≈ $641.86. The rate of return is then (641.86 - 513.16) / 513.16 ≈ 0.2507 or 25.07%, which is closest to the option B, 24.78%. The discrepancy in the final percentage is due to rounding during the calculation steps.

You Have Just Purchased a 7-Year Zero-Coupon Bond with a Yield