Question

Beam Inc. bonds are trading today for a price of

​$2,081.24.

The bond currently has

18

years until maturity and has a yield to maturity of

2.48​%.

The bond pays annual coupons and the next coupon is due in one year. What is the coupon rate of the​ bond?

Answer 1

Assuming the face value at $ 1000.

Price of bonds = Coupen Amount * Present value annuity factor ( rate of interest, number of years ) + Face value * Present value interest factor ( rate of interest, number of years )

2081.24 = Coupen Amount * PVAF (2.48%, 18) + 2000 * PVIF (2.48%, 18)

2081.24 = Coupen Amount * [ 1/1.0248 + 1/1.0248² +......+ 1/1.0248¹⁸ ] + 2000 * [ 1/1.0248¹⁸ ]

2081.24 = Coupen Amount * 14.3782 + 2000 * 0.6434

2081.24 = Coupen Amount * 14.3782 + 1286.80

Coupen Amount = ( 2081.24 - 1286.80 ) / 14.3782

Coupen Amount = $ 55.25

Coupen rate = 55.25 / 2000

                  = 2.76% Answer