How long will it take to pay off a mortgage?

Question

If a mortgage principal is $200,000, interest rate is 3.50% and the payment is $900 a month. Is there an equation to find how many payments it would take to pay off the loan?

Edit 1

I have tried to solve n and have not been able too. So I tried just solving P to see if your equation comes out with a 1000 and it does not appear to.

I wrote your equation in Python to solve P as shown below. Maybe you can tell me what I am doing wrong?

P=1000
R=50
i=0.04
n=20
print (1-(1+i/12)**n)/(i/12)*R
#The above prints out -1032.30906873

Thank you for your help.

Answer 1

Yes, $P=(\frac{1-(1+i)^{-n}}{i})R$. R is how much you pay per period (\$ 900), P is your principal (\$ 200000), and i is your interest rate per period ($\frac{0.035}{12}$). Now solve for n to compute how many months it takes to pay this mortgage off.

Answer 2

So I found the answer to my question here. So someone can mark this as a duplicate.

Anyway, thank you @Sean Nemetz for trying to help.