Fix formula RATE.

Author: grin0c

lib/financial.js

@@ -798,40 +798,30 @@ exports.RATE = function(periods, payment, present, future, type, guess) {
   }
 
   // Set maximum epsilon for end of iteration
-  var epsMax = 1e-10;
+  var epsMax = 1e-6;
 
   // Set maximum number of iterations
-  var iterMax = 50;
-
-  // Implement Newton's method
-  var y, y0, y1, x0, x1 = 0,
-    f = 0,
-    i = 0;
+  var iterMax = 100;
+  var iter = 0;
+  var close = false;
   var rate = guess;
-  if (Math.abs(rate) < epsMax) {
-    y = present * (1 + periods * rate) + payment * (1 + rate * type) * periods + future;
-  } else {
-    f = Math.exp(periods * Math.log(1 + rate));
-    y = present * f + payment * (1 / rate + type) * (f - 1) + future;
-  }
-  y0 = present + payment * periods + future;
-  y1 = present * f + payment * (1 / rate + type) * (f - 1) + future;
-  i = x0 = 0;
-  x1 = rate;
-  while ((Math.abs(y0 - y1) > epsMax) && (i < iterMax)) {
-    rate = (y1 * x0 - y0 * x1) / (y1 - y0);
-    x0 = x1;
-    x1 = rate;
-    if (Math.abs(rate) < epsMax) {
-      y = present * (1 + periods * rate) + payment * (1 + rate * type) * periods + future;
-    } else {
-      f = Math.exp(periods * Math.log(1 + rate));
-      y = present * f + payment * (1 / rate + type) * (f - 1) + future;
-    }
-    y0 = y1;
-    y1 = y;
-    ++i;
+
+  while (iter < iterMax && !close) {
+    var t1 = Math.pow(rate + 1, periods);
+    var t2 = Math.pow(rate + 1, periods - 1);
+
+    var f1 = future + t1 * present + payment * (t1 - 1) * (rate * type + 1) / rate;
+    var f2 = periods * t2 * present - payment * (t1 - 1) *(rate * type + 1) / Math.pow(rate,2);
+    var f3 = periods * payment * t2 * (rate * type + 1) / rate + payment * (t1 - 1) * type / rate;
+
+    var newRate = rate - f1 / (f2 + f3);
+
+    if (Math.abs(newRate - rate) < epsMax) close = true;
+    iter++
+    rate = newRate;
   }
+
+  if (!close) return Number.NaN + rate;
   return rate;
 };