Question

Suppose a​ five-year,$1,000 bond with annual coupons has a price of $901.51 and a yield to maturity of 6.4%.What is the​ bond's coupon​ rate?

Answer 1

Bond's price is PV of redemption price and PV of coupon payments
Bond Price	901.51
Redemption value	1000
Time	5
coupon rate	R
YTM	6.40%
PV of redemption price	=1000/(1+6.4%)^5	733.3172
So rest PV belongs to Coupon payments	=901.51-733.317
	168.193
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
PV of coupon payments	=PMT x (((1-(1 + r) ^- n)) / i)
168.193	=PMT x (((1-(1 + 6.4%) ^- 5)) / 6.4%)
168.193	=PMT x 4.1669
Annual Coupon rate=	168.193/4.1669
Annual Coupon amount=	40.36406
Annual Coupon RATE=	40.364/1000
Annual Coupon RATE=	4.04%