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What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face...

What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face value and a price of $9,350 when released?

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Answer #1

Price of zero coupon bond = Par value * 1 / (1 + YTM)n

n = number of years to maturity = 1

YTM = yield to maturity

Par value = $10,000

Price of a zero coupon bond = $9,350

$9,350 = $10,000 * 1 / (1 + YTM)1

(1 + YTM) = $10,000 / $9,350

1 + YTM = 1.0695187

YTM = 0.0695187

YTM = 6.95187% or

YTM = 6.952% (rounded off to '3' decimals)

So, Yield to maturity = 6.952%

Cross check.

Price * (1 + YTM) should be equal to par value in one year time period

$9,350 * 1.06952 = $10,000

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