Question

Answer the question on the basis of the following information for a bond having no expiration date: bond price = $1,000; bond fixed annual interest payment = $100; bond annual interest rate = 10 percent.
Refer to the given information. If the price of this bond increases to $1,250, the interest rate will:
a) fall to 9 percent.
b) fall to 8 percent.
c) rise to 11 percent.
d) rise to 12 percent.

Answer 1

Answer:

b) fall to 8 percent.

Explanation:

First, irrespective of the duration of the bond, if the price is equal to the bond's face value, it means that the coupon rate is equal to the yield to maturity (YTM).

Initial YTM = 10%

Since this is a perpetually coupon paying bond, you use PV of perpetuity  to find the rate;

PV = Coupon PMT / rate

Given PV as $1,250, new annual rate would be;

1,250 = 100/rate

solve for rate by cross multiplying;

1,250rate = 100

divide both sides by 1,250

rate = 100/1,250

rate = 0.08 or 8%

Therefore, the

interest rate would fall to 8 percent.