The equation can be solved using financial calculators or spreadsheet software. In this case, the YTM is approximately 6.17%.
Calculating Yield to Maturity (YTM)
Given:
Coupon rate = 6.50%
Maturity = 18 years
Price = $1,035.25
Par value = $1,000
Payment frequency = Semi-annual (2 times per year)
Steps:
Calculate the semi-annual coupon payment:
Coupon payment = Coupon rate * Par value / Payment frequency
Coupon payment = 0.065 * $1,000 / 2
Coupon payment = $32.50
Calculate the number of semi-annual periods:
Number of periods = Maturity * Payment frequency
Number of periods = 18 years * 2
Number of periods = 36
Use the bond pricing formula to solve for YTM:
Bond Price = PMT * [(1 - (1 + YTM/2)^-N) / (YTM/2)] + Par value / (1 + YTM/2)^N
Where:
PMT is the semi-annual coupon payment
YTM is the yield to maturity (expressed as a semi-annual rate)
N is the number of semi-annual periods
1,035.25 = 32.50 * [(1 - (1 + YTM/2)^-36) / (YTM/2)] + 1,000 / (1 + YTM/2)^36
This equation can be solved using financial calculators or spreadsheet software.
In this case, the YTM is approximately 6.17%.