# 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. Not sure how much help you're asking for... YTM = 6.1% means annual return (or effective annual) rate. Are you able to calculate the equivalent semi-annual rate? 3. 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 4. Problem can be treated as a loan of$1038.00, calling for 29 semiannual
payments of $32.03, leaving exactly$1000.00 owing after 29th payment;
in bank statement format, it'll all look a bit like this:
Code:
 N      PAYMENT    INTEREST      BALANCE
0                               1038.00
1      -32.03       31.19       1037.16
2      -32.03       31.16       1036.29
...
28      -32.03       30.16       1001.92
29      -32.03       30.11       1000.00
The payments are really the coupon amounts.
The interest is assumed as 6.1% annual effective,
thus ~3.00486% compounded semiannually:
(1 + i)^2 = 1.061
i = 1.061^(1/2) - 1
i = .0300485....

Calculation of coupon amount is this way:
(c=coupon amount, i=semiannual interest rate)

u = present value of 1000: 1000 / (1 + i)^29
v = present value of coupons: c[1 - 1/(1 + i)^29] / i
u + v = 1038 : solve for c

Hope that helps....and that Sir Jonah agrees...