Question

# You purchase a zero coupon bond with 21 years to maturity and a yield to maturity...

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

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”

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