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

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 - 1

                                    = (1 + 0.03613 - 1

                                   = 1.0736 - 1

                                     = 0.0736 or 7.36%

Therefore the effective annual rate is gotten to be 7.36%