Question

You purchase a zero coupon bond with 21 years to maturity and a yield to maturity of 5.53 percent. The bond has a par value of $1,000. What is the implicit interest for the first year? Assume semiannual compounding.

$17.24

$17.39

$17.83

$15.60

$17.12

Answer 1

Step-1, Price of the Zero-Coupon Bond at 21 Years to maturity

Par Value = $1,000

Semi-annual Yield to Maturity (YTM) = 2.765% [5.53% x ½]

Number of period = 42 Years [21 Years x 2]

The Value of the Bond = Par Value / (1 +YTM)ⁿ

= $1,000 / (1 + 0.02765)⁴²

= $1,000 / 3.14412

= $318.06

Step-2, Price of the Zero-Coupon Bond at 20 Years to maturity

Par Value = $1,000

Semi-annual Yield to Maturity (YTM) = 2.765% [5.53% x ½]

Number of period = 40 Years [20 Years x 2]

The Value of the Bond = Par Value / (1 +YTM)ⁿ

= $1,000 / (1 + 0.02765)⁴⁰

= $1,000 / 2.97721

= $335.89

Step-3, Implicit Interest for the first year

Therefore, Implicit interest for the first year = Price of the Zero-Coupon Bond at 20 Years to maturity - Price of the Zero-Coupon Bond at 21 Years to maturity

= $335.89 - $318.06

= $17.83

“Hence, The Implicit interest for the first year would be $17.83”