Question

Assume that you wish to purchase a 20 year semiannual coupon bond that has a face value of $1,000 and annual coupon rate of 8%.

If yield to maturity is 10%, What is the price of the bond(rounding to the nearest dollar)?

a) $619

b) $674

c) $761

d) $828

e) $902

Answer 1

Answer is $828

Face Value = $1,000

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $1,000
Semiannual Coupon = $40

Time to Maturity = 20 years
Semiannual Period = 40

Annual YTM = 10.00%
Semiannual YTM = 5.00%

Price of Bonds = $40 * PVA of $1 (5%, 40) + $1,000 * PV of $1 (5%, 40)
Price of Bonds = $40 * (1 - (1/1.05)^40) / 0.05 + $1,000 * (1/1.05)^40
Price of Bonds = $40 * 17.159086 + $1,000 * 0.142046
Price of Bonds = $828

So, price of the bond is $828