pmt = (r + r/((1+r)^360 - 1)) * 500000

pmt * bal = r + r/((1+r)^360 - 1)
pmt * bal = r * (1 + 1 /((1+r)^360 - 1))

p*b*r = 1 + ( 1 / ( (1+r)^360 - 1 )

p*b*r - 1 = 1 / ( (1+r)^360 - 1 )

1 / (p


m = p * ( j / (1 - (1+j)^(-360)))
m / p = j / (1 - (1+j)^(-360)))

( (1 - (1+j)^(-360))) * m) / p = j



m = p * J / ( 1 - ( 1 + j )^-n)

m - m * (1 + j)^-n = p * j


M = P * ( J / (1 - (1 + J) ** -N))
m/p = j / ( 1 - (1+j)^-n )