# Thread: Calculating the coupon rate

1. ## Calculating the coupon rate

I am stuck trying to figure out how to calculate the coupon rate. The examples I have found do not have it as an unknown.
Please help! You don't need to use my numbers. I just want to know how to solve.

Here's what is given:
14.5 years to maturity, semi-annual payments
CURRENT price of the bond is $1038 YTM = 6.1% Question: what must be the coupon rate? Thank you SO much in advance. 2. Originally Posted by valval I am stuck trying to figure out how to calculate the coupon rate. The examples I have found do not have it as an unknown. Please help! You don't need to use my numbers. I just want to know how to solve. Here's what is given: 14.5 years to maturity, semi-annual payments CURRENT price of the bond is$1038
YTM = 6.1%

Question: what must be the coupon rate?

Thank you SO much in advance.
Given the YTM (=0.061 or 6.1%), the Bond Price (P=1038) is given by
P = I PVa(YTM/2, 29) + M PVs(YTM/2, 29)
where I is the periodic bond income (= M * semi-annual coupon rate), M is the maturity value (I would assume \$1000), PVa is the Present Value for an annuity
PVa(i,n) = $\frac{1 - (1+i)^{-n}}{i}$
and PVs is the simple present value
PVs(i,n) = $\frac{1}{(1+i)^{n}}$
while i is the period interest rate and n is the period. Solve that equation for the semi-annual coupon rate and convert it to an annual rate.

You might want to look at
http://www.investopedia.com/terms/y/yieldtomaturity.asp