A bond with a 12 percent quarterly coupon rate has a yield to maturity of 16 percent. The bond has a par value of $1,000 and matures in 20 years. Based on this information, a fair price of thisbond is $____.

Question

Quizplus · Accepted Answer

The price of the bond can be calculated using the following formula:

P = (C / r) * [1 - 1 / (1 + r)^n] + FV / (1 + r)^n

Where:
P = price of bond
C = coupon payment per quarter = par value * annual coupon rate / 4 = $30
r = yield to maturity per quarter = 16% / 4 = 4%
n = number of quarters until maturity = 20 * 4 = 80
FV = face value or par value of bond = $1,000

Substituting the values in the formula, we get:

P = (30 / 0.04) * [1 - 1 / (1.04)^80] + 1000 / (1.04)^80
P = $761.49

Therefore, the fair price of the bond is $761. Round it off to the nearest dollar, thus the answer is C) 761.

A Bond with a 12 Percent Quarterly Coupon Rate Has