Question

There is a bond that has a quoted price of 105.039 and a par value of $2,000. The coupon rate is 6.87 percent and the bond matures in 25 years. If the bond makes semiannual coupon payments, what is the effective annual interest rate?

Answer 1

Par Value = $2,000

Current Price = 105.039% * $2,000
Current Price = $2,100.78

Annual Coupon Rate = 6.87%
Semiannual Coupon Rate = 6.87% / 2
Semiannual Coupon Rate = 3.435%

Semiannual Coupon = 3.435% * $2,000
Semiannual Coupon = $68.70

Time to Maturity = 25 years
Semiannual Period = 50

Let Semiannual YTM be i%

$2,100.78 = $68.70 * PVIFA(i%, 50) + $2,000 * PVIF(i%, 50)

Using financial calculator:
N = 50
PV = -2100.78
PMT = 68.70
FV = 2000

I = 3.2305%

Semiannual YTM = 3.2305%

Effective Annual Rate = (1 + Semiannual YTM)^2 - 1
Effective Annual Rate = (1 + 0.032305)^2 - 1
Effective Annual Rate = 1.0657 - 1
Effective Annual Rate = 0.0657 or 6.57%

answered by: anonymous