r' = r ^ (1/12), the monthly rate
T' = 12 * T, the number of months

B(0) = P
B(i + 1) = r' * B(i) - x
B(T') = r' * B(T' - 1) - x = 0

i    B(i)
0    P
1    r'P - x
2    r'r'P - r'x - x
3    r'r'r'P - r'r'x - r'x - x
...
k    (r' ^ k) * P - x * (r' ^ k - 1) / (r' - 1)

(r' ^ T') * P - x * (r' ^ T' - 1) / (r' - 1) = 0
x = P * (r' ^ T') * (r' - 1) / (r' ^ T' - 1)