Question

4. You find a zero coupon bond with a par value of $10,000 and 20 years to maturity. If the yield to maturity on this bond is 4.6 percent, what is the price of the bond? Assume the bond makes semiannual coupon payments.

Answer 1

Solution to QUESTION-4

Price of the Zero-coupon bond

Here, we’ve Par Value of the Bond = $10,000

Semi-annual Yield to Maturity (YTM) of the Bond = 2.30% [4.60% / 2]

Maturity period/Time to Maturity (n) = 40 Years [20 Years x 2]

Therefore, the Price of Zero-Coupon Bond = Par Value / (1 + YTM)ⁿ

= $10,000 / (1 + 0.0230)⁴⁰

= $10,000 / (1.0230)⁴⁰

= $10,000 / 2.483278043

= $4,026.94

“Hence, the Price of the Zero-coupon bond will be $4,026.94”