A zero coupon bond with a face value of $1,000 is currently selling for $687.38.The bond has a market yield of 5.48%.What is the bond's term to maturity?

Question

Quizplus · Accepted Answer

The term to maturity of a zero coupon bond can be calculated using the formula for the present value of a zero coupon bond: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value ($687.38), FV is the face value ($1,000), r is the yield (5.48% or 0.0548), and n is the number of years to maturity. Rearranging the formula to solve for n gives us $n = \frac{\log(\frac{FV}{PV})}{\log(1 + r)}$. Plugging in the values gives $n = \frac{\log(\frac{1000}{687.38})}{\log(1 + 0.0548)}$, which calculates to approximately 6.93 years.

A Zero Coupon Bond with a Face Value of $1,000