So this might seem a bit fundamental, but in financial math the following equation gives you the price for a bond
$$ P = C \frac {1-(1+i)^{-n}} {i} + B(1+i)^{-n} $$ where $P$ is the price of the bond, $C$ is the coupon bond (the payment you get for buying the bond), $B$ is the Bond's value, and $i$ is the interest rate. So naturally $ P,C,B \in \mathbb R $ and $ i \in (0,1) $.
Now my question is, how would one solve for the variable $i$ ? This should an algebraic question, which is why I am putting it here.
What I tried so far, is to do what is common to questions like this and sub $v = (1+i)^{-1} $.
and get $$ P = C \frac {1-v^n}{i} + Bv^n $$ and then reduce it to $$P-C = \frac{ v^n (C- iB) } {i} $$
I feel like there is a way to solve this through taylor expansion for $(1+i)^n$, but I have no clue D:
Again I need the equation to be rearranged for $i$.
Setting $X=1+i$, you get $$ P X^n= C \frac {X^n-1} {X-1} + B \tag1 $$ giving an algebraic equation of the form $$ P X^{n+1}-(P+C) X^{n}- B X+B+C= 0 \tag2 $$ then use numerical algorithm (using for example Newton's method) to find the apropriate root (in many cases:$0<X<2$) since when $n$ is great, you don't have a general finite formula (with radicals) for the solution.