Final answer:
The yield to maturity (YTM) of a zero coupon bond with a present value of $425.13, a par value of $1,000, and 13 years to maturity with semiannual compounding is approximately 7.03%.
Step-by-step explanation:
To calculate the yield to maturity (YTM) of a zero coupon bond that sells for $425.13, has a par value of $1,000, and matures in 13 years with semiannual compounding, we can use the following formula:
Present Value = Par Value / (1 + r)^n,
where Present Value is $425.13, Par Value is $1,000, r is the yield to maturity per period, and n is the total number of compounding periods.
Since the bond is compounded semiannually, there are 26 periods (13 years × 2). We need to solve for r in the formula:
$425.13 = $1,000 / (1 + r)^26
By transposing the formula, we get: (1 + r)^26 = $1,000 / $425.13
(1 + r)^26 = 2.3522
We can now use a financial calculator or logarithms to solve for r:
r = (2.3522)^(1/26) - 1
r = 0.035128 or 3.5128%
Since this is the semiannual yield, we need to double it to get the annual yield:
YTM = 2 × 3.5128% = 7.0256% or approximately 7.03%
Therefore, the yield to maturity for this bond with semiannual compounding is approximately 7.03%.