Question

If the fair price for a 4-year annuity paying $100 per year is $334.57, what is the yield to maturity on a four year zero–coupon bond?

Answer 1

Answer:

YTM = 8%

Explanation:

$100 per year up to 4 years means, each year, the FV = $100.

We know, Zero coupon bond = [Fair Value ÷ $(1 + YTM)^{n}$]

As the 4-year annuity paying the different YTM in the previous three years, 4th year YTM will be -

Bond value = $\frac{100}{1 + 0.6}$ + $\frac{100}{(1+0.07)^2}$ + $\frac{100}{(1+0.08)^3}$ + $\frac{100}{(1+YTM{4})^4}$

or, $334.57 = $94.3396 + $87.3439 + $79.3832 + $\frac{100}{(1+YTM{4})^4 }$

or, $334.57 - 261.0667 = $\frac{100}{(1+YTM{4})^4 }$

or,  $(1+YTM{4})^4$ = ($100 ÷ $73.50)

or, 1 + YTM = $(1.3605)^{\frac{1}{4}}$

or, YTM = 1.08 - 1

YTM = 0.08 or 8%