Question

A zero coupon bond with a face value of $1,000 is issued with an initial price of $492.96. The bond matures in 15 years. What is the implicit interest, in dollars, for the first year of the bond's life? Use semiannual compounding.

Answer 1

Price of a bond is present value of all the cashflows associated with the bond - namely coupons and maturity value.

Mathematically,

In the question above, we first need to calculate the rate of interest or yield.

F = $1000, Bond value = $492.96, t = 15 years = 30 semi-annual periods

Substituting these values in mathematical relation above,

(1 + r)³⁰ = 2.02856

1 + r = 1.02386

r = 0.02386 = 2.386% --> This is semi-annual yield or rate.

Now, we need to calculate the value of bond at the end of year 1 using the calculated rate of interest.

FV = PV * (1 + r)ⁿ

PV or the current price of bond = $492.96, Number of periods = 2 semi-annual periods (since 1 year)

FV (at end of year 1) = 492.96 * (1 + 0.02386)²

FV (at end of year 1) = $516.7624

Implied Interest is hence = $516.7624 - 492.96 = $23.8024