Question

What is the price of a 10-year bond paying an annual coupon rate of 8.6%, but paying it semiannually, per face (par) value of $1,000 if the annual market rates for these bonds are 12.1%? Answer to the nearest cent, xxx.xx

What is the price of a 12-year bond paying 8.2% annual coupons with a face (par) value of $1,000 if the market rates for these bonds are 11.6%? Answer to the nearest cent, xxx.xx

Answer 1

1)

Coupon = (8.6% of 1000) / 2 = 43

Number of periods = 10 * 2 = 20

Rate = 12.1% / 2 = 6.05%

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

Price = 43 * [1 - 1 / (1 + 0.0605)^20] / 0.0605 + 1000 / (1 + 0.0605)^20

Price = 43 * [1 - 0.308878] / 0.0605 + 308.877692

Price = 43 * 11.423509 + 308.877692

Price = $800.09

2)

Coupon = 8.2% of 1000 = 82

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

Price = 82 * [1 - 1 / (1 + 0.116)^12] / 0.116 + 1000 / (1 + 0.116)^12

Price = 82 * [1 - 0.267935] / 0.116 + 267.935133

Price = 82 * 6.310904 + 267.935133

Price = $785.43