Question

You have just purchased a regular bond. The has a face value of $400,000. The bond has a coupon rate of 5.1%. Coupons are paid annually. The yield to maturity on the bond is 4.8%. The bond has 22 years to maturity. How much did you pay for the bond today?

Answer 1

Solution

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Face value =400000

n=number of periods to maturity=22

r-intrest rate per period=4.8%

annual Coupon payment=coupon rate *face value=5.1%*400000=20400

Price of bond=?

Putting values in formula

Price of bond=20400*((1-(1/(1+4.8%)^22))/r)+400000/(1+4.8%)^22

Solving we get

Price of bond today=416087.66

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