Question

A $1,000 bond has a 6% annual coupon paid semi-annually. The bond has a ten-year maturity and was issued two years ago. What is the current price of this bond at these current interest rates: 7%, 5%, and 3%?

Answer 1

Face Value of Bond = F = $ 1000

Annual coupon rate = 6%, semi-annual coupon rate = 6%/2 =3%

Therefore, semi-annual Coupon payment = C = 3% * 1000 = 30

Sine the bond has a ten year maturity and it was issued 2 years ago. So, 8 years are remaining till maturity or 16 semi-annual coupon payments till maturity.

We know that for a bond with n periods of coupon payments till maturity, the coupon payment will be C till the nth period along with a cash flow of face value F (Face value of the bond) at the nth period. So in order to calculate the present value of the bond, we will have to calculate the present value of these future cash flows. and the present value is calculated using the following discounting formula:

where C is the cashflow at nth period.

Therefore, the current price of the bond is calculated using the below formula:

where F is the face value of the bond, C is the coupon payments, r is the interest rate and n is the total coupon payments till maturity.

Case I

Annual interest rate = 7% Since the coupons are paid semi-annualy so, semi-annual interest rate = r = 7%/2 = 3.5%

C = $30

F = $1000

Case II

Annual interest rate = 5% Since the coupons are paid semi-annualy so, semi-annual interest rate = r = 5%/2 = 2.5%

C = $30

F = $1000

Case III

Annual interest rate = 3% Since the coupons are paid semi-annualy so, semi-annual interest rate = r = 3%/2 = 1.5%

C = $30

F = $1000

Answer:

Interest Rate	Bond Price
7%	939.529416
5%	1065.275013
3%	1211.968961