Answer:
To calculate the yield to maturity (YTM) of a bond, we need to find the interest rate at which the present value of the bond's future cash flows equals its current market price.
In this case, the bond has:
Face value (FV) = $1000
Coupon rate (CR) = 8.5% or 0.085
Semiannual coupons
Time to maturity (n) = 10 years, but since coupons are paid semiannually, there are 20 periods.
The bond is trading for $1034.74.
Using a financial calculator or spreadsheet, we can use the present value of an annuity formula:
PV = C * [1 - (1 + r)^(-n)] / r + FV / (1 + r)^n
Where:
PV = Present value (market price)
C = Coupon payment per period
r = Yield to maturity rate (expressed as a semiannual rate)
n = Total number of periods
FV = Face value
Substituting the given values:
1034.74 = 42.5 * [1 - (1 + r)^(-20)] / r + 1000 / (1 + r)^20
To solve for r (the semiannual yield to maturity), we can use iterative methods or financial calculators.
The approximate yield to maturity calculated using iterative methods or financial calculators is approximately 4.075% (as a semiannual rate). Doubling this gives us the annual yield to maturity.
YTM (APR) ≈ 4.075% * 2 = 8.15%
So, the closest option is:
A) 8.15%
