How Interest Rate Changes Affect Coupon Bond Prices
Summary
The document distinguishes pricing a finite-maturity coupon bond from valuing an infinite-lived stream of coupons. For the example, a bond with a $1,000 face value pays $100 annually for ten years. If the discount rate falls to 5%, its price is the present value of those coupons plus the repayment of principal at maturity, calculated in the question as $1,386. The accepted explanation says the $2,000 figure instead comes from treating the bond as a perpetuity: an endless $100 coupon stream discounted at 5% has value $100 divided by 0.05.
The key lesson is that a bond’s maturity and principal repayment matter when discounting its cash flows. The perpetuity calculation does not describe the finite bond in the example. The document offers a conceptual clarification rather than a full discussion of yield curves, coupon timing, credit risk, or market pricing, so its figures depend on the simplified assumptions given.
Key ideas
- A finite-maturity bond is valued by discounting its coupons and principal repayment.
- A perpetuity has no maturity and can be valued as its constant coupon divided by the discount rate.
- The perpetuity valuation explains the $2,000 example, while the finite bond’s stated present value is $1,386.
- Bond price calculations depend on which cash flows and maturity assumptions apply.
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Full text
# Pricing a government bond
# Pricing a government bond
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?
## Answer by Cornholio (score 3, accepted)
https://quant.stackexchange.com/a/46929
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 $\frac{100}{0.05}=2000$.
## Answer by user11823918 (score 1)
https://quant.stackexchange.com/a/46928
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.)Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.