If you have just purchased a 4-year zero coupon bond,what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value of the bond = $1,000)

Question

Quizplus · Accepted Answer

A zero coupon bond does not pay interest, but it is purchased at a discount and pays its par value at maturity. The expected rate of return on a zero coupon bond can be calculated using the formula:
(Par value/Purchase price)^(1/years to maturity) - 1

For a 4-year zero coupon bond, the purchase price would be:
Purchase price = Par value / (1 + implied rate)^4

Since the implied forward rates stay the same, the rate used to calculate the purchase price would be the current 4-year implied forward rate.
If we assume the current 4-year implied forward rate is 3%, we can calculate the purchase price as follows:
Purchase price = $1,000 / (1 + 0.03)^4 = $822.70

Then, the expected rate of return in the first year can be calculated as:
($1,000 / $822.70)^(1/4) - 1 = 0.0275 or 2.75%

Therefore, the best choice is B, with an expected rate of return of 3%, which is the closest to the calculated rate using the formula above.

If You Have Just Purchased a 4-Year Zero Coupon Bond,what