Question

A zero coupon bond with a face value of $1,000 is issued with a initial price of $333.33. The bond matures in 23 years. What is the 3-year implicit interest, in dollars, from the 7th to the 10th year of the bond’s life? The bond’s yield is semiannually compounded.

Answer 1

Answer:

Price of zero coupon bond = F/(1+r)^n

F = $1000

Price = $333.33

n = 23 years = 46 periods

333.33 = 1000/((1+r)^46

r = 2.42% semiannually

We need to find interest from year 7 (period 14) to year 10 (period 20)

Price after period 14 = F/(1+r)^n = 1000/(1.0242)^(46-14) = $465.25

Price after period 15 = F/(1+r)^n = 1000/(1.0242)^(46-15) = $476.51

Price after period 16 = F/(1+r)^n = 1000/(1.0242)^(46-16) = $488.04

Price after period 17 = F/(1+r)^n = 1000/(1.0242)^(46-17) = $499.85

Price after period 18 = F/(1+r)^n = 1000/(1.0242)^(46-18) = $511.95

Price after period 19 = F/(1+r)^n = 1000/(1.0242)^(46-19) = $524.34

Implicit interest from year 7 to 10 = 0.0242($465.25 + $476.51 + $488.04 + $499.85 + $511.95 + $524.34)

= $71.78