How do you benefit from a fall in interest rates in general as a creditor of public bonds?

Question

I’m reading about England debt in 1819 and how interest rate benefited its creditors. The country had a public debt of more than 250% of the GDP.

With peace at last achieved, London is faced with a mountain of debt that it intends to repay.  And for good reason: it is owned by the aristocracy and the most influential members of Parliament (they will not fail to make huge gains on their "consols" (consolidated bonds) thanks to the fall in interest rates,  the Rothschild's fortune dates from these days)

How does the creditors of those consolidated bonds benefited from a fall in interest rates ? How do you benefit from a fall in interest rates in general as a creditor of public bonds?

1muflon1 · Accepted Answer

This is because bond prices increase when interest rate falls.
A general bond pricing formula can be expressed as as a discounted stream of future cash flows from the coupon and the value of the bond itself. Hence we have:
$$ P = sum^T_{t=1} frac{C_t}{(1+i)^t}+frac{M}{(1+i)^T}$$
Where $P$ is the price of the bond, $C$ is the coupon $i$ the interest rate, and $M$ the value at maturity (i.e. the face value). You can also learn more about the formula here if you are interested.
As you can see from the above formula when $i$ increases $P$ decreases and vice versa.  Hence fall in the interest rate is good for you if you are a bond holder as now you can sell your bond on secondary market for more than before.

How do you benefit from a fall in interest rates in general as a creditor of public bonds?

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