Assuming a mortgage has annual interest of rate r, after how many months have you paid off half the principal amount? In other words, if you have a 200,000 USD loan at 4% over 30 years. After how many monthly payments do you only owe 100,000?

Write a python program where you experiment with varying values of the interest rate r and the loan period N, which is usually 360 months for 30 years and 180 months for 15 years, but it could be any positive integer. See if you can find a formula as a function of r and N.