A bond with a coupon rate of 4,875%, yield to maturity of 4,727%, face value of $1,000. The quoted price for the bond is $101,203. What is the maturity of the bond?
Assistance needed.
If it makes you feel any better, I have no idea how to do this either.
To calculate the maturity of the bond, we need to find the number of years remaining until the bond reaches its maturity date.
The coupon rate of 4,875% and the face value of $1,000 suggest that the bond pays an annual coupon payment of 4,875/100 * $1,000 = $48.75.
The yield to maturity (YTM) of 4,727% represents the effective annual interest rate that a bondholder will earn on the bond if held until maturity.
The quoted price for the bond is $101,203, which suggests that the market value of the bond is currently higher than its face value.
To find the number of years until maturity, we can use the following formula:
PV = C * (1 - 1 / (1 + r)^n) / r + F / (1 + r)^n
Where:
PV = Present value or quoted price of the bond ($101,203)
C = Annual coupon payment ($48.75)
r = Yield to maturity (0.04727)
n = Number of years until maturity (what we need to find)
F = Face value of the bond ($1,000)
We can rearrange the formula to solve for n:
n = log(F / (F - PV * r)) / log(1 + r)
Plugging in the given values:
n = log(1000 / (1000 - 101,203 * 0.04727)) / log(1 + 0.04727)
After calculating this expression, we find that the maturity of the bond is approximately 11.73 years.