Question

compute the price if a 5.7% coupon bond with 15 years left to maturity and a market interest rate of 9.2% (assume interest payments are semiannual)

please show work

Answer 1

Face Value = $1,000

Annual Coupon Rate = 5.70%
Semiannual Coupon Rate = 2.85%
Semiannual Coupon = 2.85% * $1,000
Semiannual Coupon = $28.50

Time to Maturity = 15 years
Semiannual Period = 30

Annual Interest Rate = 9.20%
Semiannual Interest Rate = 4.60%

Current Price = $28.50 * PVIFA(4.60%, 30) + $1,000 * PVIF(4.60%, 30)
Current Price = $28.50 * (1 - (1/1.0460)^30) / 0.0460 + $1,000 * (1/1.0460)^30
Current Price = $28.50 * 16.098968 + $1,000 * 0.259447
Current Price = $718.27