Financial math: calculation of mortgage interest rate

Self-tutoring about financial math: the tutor mentions the mortgage interest rate.

I was looking at the formula for the periodic payment of a mortgage:

P=(-1(r/n))*L*(1+r/n)^(nt)/(1-(1+r/n)^(nt))

P=payment

r=rate

n=payments per year (and compounding periods per year as well)

t=years

Specifically I was wondering if it can be rendered, algebraically, to be a formula for r, the rate. However, I don’t think it can.

To “get r by itself”, you’d have to take the (nt)^th root of the terms (1+r/n)^(nt). Yet, there is also a term on the top, r/n, which won’t root out at the same time. Therefore, I suspect that formula can’t be solved for r.

“But Jack,” someone might say, “why would you even think about that? Everyone uses financial calculators or computer apps to calculate such a value.” Yes, true: the idea is academic, which is exactly why I bring it up:)

Source:

thebalance.com