What must be the price of a $1000 bond with a 5.8% coupon rate,annual coupons,and 30 years to maturity if YTM is 7.5% APR?

Question

Quizplus · Accepted Answer

To calculate the price of the bond, we need to use the present value formula:

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

Where:
C = Annual coupon payment = 5.8% * $1000 = $58
r = Yield to maturity = 7.5% APR = 0.075 / 1 = 0.075
n = Number of periods = 30
FV = Face value of the bond = $1000

Plugging in the values, we get:

PV = $58 * [(1 - (1 + 0.075)^(-30)) / 0.075] + $1000 / (1 + 0.075)^30
PV = $799.22

So the price of the bond must be $799.22, which is closest to answer choice C.

What Must Be the Price of a $1000 Bond with a 5.8