The following information relates to Questions 16-29

-The one-year spot rate r(1) = 5% and the forward price for a one-year zero-coupon bond beginning in one year is 0.9346. The spot price of a two-year zero-coupon bond is closest to:
A) 0.87.
B) 0.89.
C) 0.93.

Question

The following information relates to Questions 16-29
 
-The one-year spot rate r(1) = 5% and the forward price for a one-year zero-coupon bond beginning in one year is 0.9346. The spot price of a two-year zero-coupon bond is closest to:
A) 0.87. 
B) 0.89. 
C) 0.93.

Quizplus · Accepted Answer

The spot price of a two-year zero-coupon bond can be found by discounting the cash flow of receiving $1 in two years back to the present using the spot rates. Alternatively, we can use the formula for the spot rate of a two-year bond:

r(2) = [(1 + r(1))^2 × 1 - F(1, 1)] / F(1, 2)

where F(1, 1) is the forward price for a one-year zero-coupon bond beginning in one year and F(1, 2) is the forward price for a two-year zero-coupon bond beginning in one year.

We are given that r(1) = 5% and F(1, 1) = 0.9346. We can solve for F(1, 2) by rearranging the formula:

F(1, 2) = [(1 + r(1))^2 × 1] / (1 + r(2))

0.9346 = [(1 + 0.05)^2 × 1] / (1 + r(2))

1 + r(2) = [(1.05)^2] / 0.9346

r(2) = 0.089 or 8.9%

Therefore, the spot price of a two-year zero-coupon bond is closest to 0.89, which is answer choice B.

The Following Information Relates to Questions 16-29