Final answer:
To calculate the yield to maturity of a zero-coupon bond, divide the face value by the current price, take the n-th root where n is the years to maturity, subtract 1, then multiply by 100 to convert to a percentage. In this case, the YTM is approximately 0.694%, so option B is correct.
Step-by-step explanation:
The question asks us to calculate the yield to maturity (YTM) of a risk-free, zero-coupon bond with a face value of $10,000, currently trading at $8,700, with 20 years to maturity. The yield to maturity is the total return expected on a bond if the bond is held until the date it matures.
To find the yield to maturity, we use the formula for YTM of a zero-coupon bond which is:
- Dividing the face value by the current price of the bond to find the total return at maturity: ($10,000 / $8,700)
- Calculate the n-th root of the total return, where n is the number of years to maturity - in this case, 20 years.
- Subtract 1 from the result of the n-th root to find the YTM.
- Multiply by 100 to convert to a percentage.
Calculating:
(1) Total return at maturity = ($10,000 / $8,700) = 1.149425287
(2) n-th root = (1.149425287)^(1/20) = 1.00694 approximately
(3) Subtracting 1 = 0.00694
(4) Convert to percentage = 0.00694 * 100 = 0.694% approximately
Therefore, the YTM of the bond is very close to 0.694%, which makes option B the correct answer.