Question

There is a bond that has a quoted price of 94.023 and a par value of $2,000. The coupon rate is 6.51 percent and the bond matures in 13 years. If the bond makes semiannual coupon payments, what is the effective annual interest rate

Answer 1

Answer:

The effective annual rate is gotten to be 7.36%

Explanation:

Given the par value = $2,000

Annual Coupon Rate = 6.51%

Semiannual Coupon Rate =  6.51%  / 2 = 3.255%

Semiannual Coupon = 3.255% * $2,000  =  $65.10

Current Price = 94.023% * $2,000  = $1,880.46

Time to Maturity = 13 years

Semiannual Period = 26

Let semiannual yield to maturity be s%

$1,880.46 = $65.10 x PVIFA(s%, 26) + $2,000 x PVIF(s%, 26)

Making use of Ms excel and calculating we have;

N = 26

PV = -1880.46

PMT = 65.10

FV = 2000

s = 3.613%

Semiannual yield to maturity = 3.613%

The effective annual rate can be obtained thus;

Effective annual rate = (1 + Semiannual YTM$)^{2}$ - 1

                                    = (1 + 0.03613$)^{2}$ - 1

                                   = 1.0736 - 1

                                     = 0.0736 or 7.36%

Therefore the effective annual rate is gotten to be 7.36%