Question

A 5-year zero coupon bond pays 10% annual coupons, and has a face value of $1,000. Zero coupon bonds with 1-5 years to maturity, each with a face value of $100, have the following prices:

Price of 1-year zero = $99.14

Price of 2-year zero = $97.88

Price of 3-year zero = $96.32

Price of 4-year zero = $89.44

Price of 5-year zero = $87.76

What is the price of the 5-year coupon bond?

Answer 1

Yield on zero coupon bond =((F/PV)^(1/n)) - 1
F = Face value
P = Present value
N = Number of years
Yield on zero coupon 5 year bond =((100/87.76)^(1/5)) - 1
Yield on zero coupon 5 year bond = 2.6457%
Yield to maturity = 2.6457%
Coupon = 1000 * 10% = 100
Years = 5
Formula for Bond price
Bond Price = Coupon * (((1 - (1 + yield to maturity)^ -n))/yield to maturity) + (Face value / (1+ yield to maturity)^n)
Bond Price = 1000 * (((1 - (1 + 2.6457%)^ -5))/2.6457%) + (1000 / (1+ 2.6457%)^5)
Bond Price = $1,340.24
Answer :
The price of the 5 year coupon bond = $1,340.24