What is the price of an annual coupon bond with 10 years to maturity, 8% coupon rate, if yield to maturity is 9%?

I can’t seem to work it out right.

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  • How are you trying to calculate it? Essentially you have to discount each cash flow to the present using the yield to maturity. – D Stanley Dec 27 '19 at 21:33
  • 1.What is the price of an annual coupon bond (face value = 1000) with 10 years to maturity, 8% coupon rate, if yield to maturity is 9%?=80×(1/9%―1/9%×(1+9%)power10)+1000/(1+9%)power10 =9 35.82... so I have this solution from one of my lecture slides but when I enter it in my calculator I get a totally different answer. What am I doing wrong? – Tee Dec 27 '19 at 21:40
  • Are you using negative exponents? (it's hard to tell from the lack of formatting) – D Stanley Dec 27 '19 at 21:46
  • ibb.co/kXFx2P6 Please check this out. I am trying to understand the formula and I am in my first year of University which is why I’m struggling a bit. – Tee Dec 27 '19 at 21:51
  • The formula is right. I suspect you are not entering it into your calculator correctly. – D Stanley Dec 27 '19 at 21:53

I am not familiar with the formula you used. The value of the bond is the present value of all its coupons plus the present value of its payments. So, if we assume that the bond is going to pay off for 100 then the present value of that payment is:
100 / (1.09^10)
The present value of the ith interest payment is:
8 /(1.09^i)
So to find the value of the bond, I add up the present value of the 10 interest payments and the final payment. I find the current value of the bond to be 93.5823.

In doing these calculations, I am assuming the bond pays interest only once a year. In the real world, most bonds pay twice a year and some bonds pay four times a year.

  • 1
    the formula is a simplification of an annual coupon paying bond. You are right in general, but the formula given yields the right answer if the operations are done in the right order. – D Stanley Dec 28 '19 at 15:03
  • @DStanley Based upon your comment, I have updated my answer. – Bob Dec 28 '19 at 15:31

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