Solving an Annuity Loan for any of the parameters with Newton Raphson

annuities.py

'''
calculate annuities 

'''

'''
 annuities kernel
 s: total amount
 r: nominal annual rate
 t: duration/years
 a: monthly payment
'''
def annuities(s,r,t,a):
    return (1+r)**t * (a-s*((1+r)**(1./12)-1)) - a


'''
 newton raphson
 kernel: kernel (function with n numeric arguments)
 params: starting parameters for the kernel
 idx: index of the parameter to be varied
 err: desired accuracy

 assuming differentiability of kernel in all 
 parameters in the vicinity of the starting values.
'''
def newtonraphson(kernel, params, idx, err=1e-6):
    dx = 1e-2*err
    p0 = params
    p1 = p0[:]
    for x in range(50):
        
        p1[idx] = p0[idx] + dx
        f0 = kernel(*p0)
        df = (kernel(*p1) - f0)/dx
        xi = f0/df
        p0[idx] -= xi
        print kernel(*p0)
        if abs(xi) < err * abs(p0[idx]):
            return p0

    print 'WARNING: Newton Raphson did not converge.'
    return None



# solve for the rate.
print newtonraphson(annuities, [10000,0.039,10,100], 1)