(10C) Mortgage Loan Interest Rate

[Albert Chan]

PHP Code:

def solve_r(i, n):  # r = payment / principle
    try: return i/(1.-(1.+i)**-n)
    except ZeroDivisionError: return 1./n 


PHP Code:

def solve_i(n, r, eps=1e-8, verbal=True, f=solve_r):
    i0 = r - 1.0/(r*n*n); f0 = f(i0, n)  # guess i0
    i1 = i0 + 1.5*(r-f0); f1 = f(i1, n)  # guess i1
    if verbal: print '%.15g =>\t%.15g' % (i0, i1)
    while f0 != f1:
        di = (i0-i1)*(r-f1)/(f0-f1); i0 = i1; i1 += di
        if verbal: print '%+.6e => \t%.15g' % (di, i1)
        if abs(di) < eps: break
        f0 = f1; f1 = f(i1, n)
    return i1 


Here is an interest finder by secant's method.
Below example (accurate to 10 places), only 3 f(i) calls are needed.

Code:

>>> solve_i(n=36, r=86.67/2500)
0.0124110212798083 =>   0.0124934261260045
+1.112498e-05 =>        0.0125045511103353
-5.107705e-09 =>        0.0125045460026299
0.012504546002629922