Final answer:
To calculate the yield to maturity on a zero-coupon bond with semiannual compounding, use the formula: YTM = [(Face Value / Present Value)^(1/n)] - 1, where face value is $10,000, present value is $4,469.32, and n is 44. Then, to get the annual rate, multiply the semiannual yield by 2.
Step-by-step explanation:
The student has asked about calculating the yield to maturity (YTM) for a zero-coupon bond with semiannual compounding. This bond has a current price of $4,469.32 and a par value of $10,000, with 22 years to maturity. To calculate the YTM, use the formula:
Bond Yield to Maturity Formula
YTM = [(Face Value / Present Value)^(1/n)] - 1
- Face Value: The par value of the bond, which for this question is $10,000.
- Present Value: The current price of the bond, which is $4,469.32.
- n: The number of compounding periods until maturity. Since the compounding is semiannual, and there are 22 years left, n = 22 * 2 = 44 periods.
Substituting the given numbers into the formula gives us:
YTM = [($10,000 / $4,469.32)^(1/44)] - 1
To obtain the semiannual yield, we need to calculate:
YTM (semiannual) = [($10,000 / $4,469.32)^(1/44)] - 1
Then, to get the annual rate, we multiply the semiannual yield by 2:
YTM (annual) = 2 * [($10,000 / $4,469.32)^(1/44)] - 1
An exact figure would require a calculator or financial software to compute.