Question

(1 point) A 6 year $13000 par-valued bond pays quarterly coupons. If the yield rate is y4-6% and the purchase price is $11763.12, what is the coupon rate c4? Answer: 2.0499981*2

Answer 1

Bond price = c x F x 1 -(1+r)^-t /r + F/(1+r)^t

c = Coupon rate

F = Face value = $ 13,000

r = Yield rate = 6 % or 0.06/4 = 0.015 per quarter

t = periods to maturity = 6 x 4 = 24

$ 11,763.12 = c x $ 13,000 x 1-(1+0.015)^-24/0.015 + $ 13,000/(1+0.15)²⁴

= c x $ 13,000 x 1 -(1.015)^-24/0.015 + $ 13,000 x (1.015)^-24

^{= c x $ 13,000 x 1 - 0.6995439195/0.015 + $ 13,000 x 0.6995439195}

^{= c x $ 13,000 x 0.3004560805/0.015 + $ 9,094.0709535628}

^{= c x $ 13,000 x 20.0304053663 + $ 9,094.0709535628}

^{= c x $ 260,395.269762482 + $ 9,094.0709535628}

^{$ 11,763.12 - $ 9,094.0709535628 = c x $ 260,395.269762482}

^{$ 2,669.0490464372 = c x $ 260,395.269762482}

^{c = $ 2,669.0490464372/$ 260,395.269762482}

^{c = 0.01249991 or 0.01249991 x 4 x 100 = 4.099996208 %}

Coupon rate is 4.099996208 %