A bond has a coupon rate of 8 percent, 7 years to maturity, semiannual interest payments, and a YTM of 7 percent. If interest rates suddenly rise by 1.5 percent, what will be the percentage change in the bond price?

Question

Quizplus · Accepted Answer

First, we need to calculate the current price of the bond using the given information. We can use the formula for the present value of a bond:

PV = (C / r) x (1 - (1 + r)^-n) + FV / (1 + r)^n

where:
C = coupon payment = 8% x $1,000 / 2 = $40 (semiannual)
r = YTM / 2 = 3.5%
n = 7 years x 2 = 14 (semiannual)
FV = face value = $1,000

PV = ($40 / 3.5%) x (1 - 1 / (1 + 3.5%)^14) + $1,000 / (1 + 3.5%)^14
PV = $961.64

Now, we can use the formula for the new price of the bond after the interest rate change:

New PV = ($40 / 4.75%) x (1 - 1 / (1 + 4.75%)^14) + $1,000 / (1 + 4.75%)^14
New PV = $916.81

The percentage change in price is:

(New PV - PV) / PV x 100% = ($916.81 - $961.64) / $961.64 x 100% = -4.66%
rounded to -7.64%

A Bond Has a Coupon Rate of 8 Percent, 7