Question

Consider three bonds with 6.70% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years.

e. What will be the price of the 8-year bond if its yield decreases to 5.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

f. What will be the price of the 30-year bond if its yield decreases to 5.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

e)

Coupon = 0.067 * 1000 = 67

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 67 * [1 - 1 / (1 + 0.057)⁸] / 0.057 + 1,000 / (1 + 0.057)⁸

Price = 67 * [1 - 0.641801] / 0.057 + 641.800575

Price = 67 * 6.2842 + 641.800575

Price = $1,062.84

e)

Coupon = 0.067 * 1000 = 67

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 67 * [1 - 1 / (1 + 0.057)³⁰] / 0.057 + 1,000 / (1 + 0.057)³⁰

Price = 67 * [1 - 0.189562] / 0.057 + 189.561607

Price = 67 * 14.218217 + 189.561607

Price = $1,142.18