The formula for the present value of an annuity is:
$$p = \frac{a[1-(1+r)^{-n}]}{r}$$
Where:
p = present value
r = discount rate
n = number of payments
I would like to find the discount rate, since I already know the number and amount of payments, which is \$3000 $\times$ 120. Unfortunately, I have run into a bit of a situation involving a polynomial. According to a similar question it is not possible to isolate $r$ on one side of the equation. I am trying to avoid using goal seek in Excel. Is it possible to plug in the other values first, and then solve for $r$?
You can write a solution in form of infinite nested radicals. If you put: $(1+r)=x $ and $a/p=M$ your equation become $$ (M+1-x)x^n=M $$ and you find: $$ x=\sqrt[n]{\dfrac{M}{M+1-x}} $$ and substituting $x$ recursively you find: $$ x=\sqrt[ n]{\dfrac{M}{M+1-\sqrt[n]{\dfrac{M}{M+1-\sqrt[n]{\dfrac{M}{M+1-\cdots }} }} }} $$ But I fear that this formula converges too slowly for an efficient computation.