A zero coupon bond with a face value of $1,000 is issued at an initial price of $375. The bond matures in 20 years. What is the implicit interest, in dollars, for the ﬁrst year of the bond's life?

Question

Quizplus · Accepted Answer

The implicit interest is the difference between the face value and the initial price, which is $625. Dividing this by the number of years until maturity (20) gives an implicit interest of $31.25 per year. However, we only want to find the implicit interest for the first year, so we need to discount this amount by the interest rate for the first year.

To find the interest rate for the first year, we can use the formula for calculating the present value of a zero coupon bond:

PV = FV / (1 + r)n

where PV is the initial price, FV is the face value, r is the interest rate, and n is the number of years until maturity. Solving for r, we get:

r = (FV / PV)1/n - 1

Plugging in the values from the problem, we get:

r = ($1,000 / $375)1/20 - 1 
r = 0.07463

So the interest rate for the first year is 7.463%. To find the implicit interest for the first year, we need to discount the total implicit interest of $31.25 by this rate:

Implicit interest for first year = $31.25 / (1 + 0.07463) 
Implicit interest for first year = $18.85

Therefore, the best choice is B) $18.85.

A Zero Coupon Bond with a Face Value of $1,000