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I am reading the "Bond" article on investopedia on stumble on the way they price a government bond.

Say that the interest rate at time $t=0$ is $r=10\%$. I buy a government bond with face value 1000\$ and maturity date 10 years from now. The yearly coupon must thus be 100\$ and the price of this bond at $t=0$ is 1000\$.

Now say that the interest falls afterwards to $r' = 5\%$. I want to sell my bond to benefit from this, what is its new price?

My reasoning is that the price of the bond is equal to its present value of $$ \frac{100}{1+r'} + \ldots + \frac{100}{(1+r')^{10}} + \frac{1000}{(1+r')^{10}} = 1386 $$ dollars, but according to investopedia (https://www.investopedia.com/terms/b/bond.asp paragrapph "Pricing Bonds") the new price is in fact 2000\$, because 5% of 2000\$ is equal to the coupon paid by my bond.

Can you help me sort this out?

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    $\begingroup$ Your calculation is correct. Investopedia entry seems confused. It is true that as maturity extends indefinitely, the price of the 10pct bond in a 5pct environment tends to 2000. Maybe that’s what they were assuming ? $\endgroup$ – dm63 Aug 2 '19 at 20:05
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    $\begingroup$ Yes, the Investopedia article (not at all clearly written) says nothing the example bond's maturity, but the calculation seems to be for perperuals. $\endgroup$ – Dimitri Vulis Aug 2 '19 at 21:44
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To make this clear. The article considers a bond that is paying a coupon infinitely, so there is no expiration. In this case, the value of the bond is the sum of the discounted coupons $\frac{100}{(1+r)}+\frac{100}{(1+r)^2}+\frac{100}{(1+r)^3}+\dots$ which eqals $\frac{100}{r}$. So in case of $r=0.10$ the bond price is $\frac{100}{0.1}=1000$ and in case of $r=0.05$ the bond price is $\frac{100}{0.05}=2000$.

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  • $\begingroup$ agreed. Is your real name Beavis? $\endgroup$ – dm63 Aug 3 '19 at 20:21
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Answer was provided to me in the comments so I may as well close the question non. My computation is right, and the Investopedia article is not saying what I thought it was. (What the article really says is still unclear.)

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