Question

Suppose you purchase a zero coupon bond with a face value of $1,000, maturing in 20 years, for $214.55. Zero coupon bonds pay the investor the face value on the maturity date. What is the implicit interest in the first year of the bond's life? The implicit interest in the first year of the bond's life is _________. (Round to the nearest cent.)

Answer 1

The Price of the zero-coupon Bond is calculated by using the following formula

Price of the zero-coupon = Face Value / (1 + YTM)ⁿ

$214.55 = $1,000 / (1 + YTM)²⁰

(1 + YTM)²⁰ = $1,000 / $214.55

(1 + YTM)²⁰ = 4.66092

YTM = 8% (From the Future Value Factor Tactor Table, we can find that the discount rate corresponding to the factor of 4.66092 for 20 Years is 8%)

Therefore, the the implicit interest in the first year of the bond's life = Price of the Bond x Yield to Maturity (YTM) of the Bond

= $214.55 x 8%

= $17.16

“The implicit interest in the first year of the bond's life = $17.16”