使用牛顿法重新创建Excel RATE函数 [英] Recreate Excel RATE function using Newton's Method

问题描述

我正在使用PHP转换抵押计算器，但不一定需要PHP解决方案。我正在寻找复制Excel RATE 函数所需的逻辑。我找到了一个使用二等分的解决方案，如果更糟糕的是，我使用这个。

I'm working on converting a mortgage calculator in PHP, but I don't necessarily need a PHP solution. I'm looking for the logic needed to replicate the Excel RATE function. I've found a solution which uses bisection, and if worse comes to worse, I use that.

我知道这个世界上有一个人知道这样一个功能，所以我希望有一个简单的答案，而不是从头开始创建一个解决方案。

I know someone out there in the interwebs world has knowledge of such a function, so I'd love to have an easy answer instead of creating a solution from scratch.

参考文献：

• http：// office。 microsoft.com/en-us/excel-help/rate-HP005209232.aspx


• http://en.wikipedia.org/wiki/Newton%27s_method

• http://office.microsoft.com/en-us/excel-help/rate-HP005209232.aspx
• http://en.wikipedia.org/wiki/Newton%27s_method

谢谢

推荐答案

使用割线法（牛顿法的有限差分近似法）实现MS Excel RATE（）函数来自PHPExcel：

Implementation of the MS Excel RATE() function using the secant method (a finite difference approximation of Newton's method) taken from PHPExcel:

define('FINANCIAL_MAX_ITERATIONS', 128);
define('FINANCIAL_PRECISION', 1.0e-08);


function RATE($nper, $pmt, $pv, $fv = 0.0, $type = 0, $guess = 0.1) {

    $rate = $guess;
    if (abs($rate) < FINANCIAL_PRECISION) {
        $y = $pv * (1 + $nper * $rate) + $pmt * (1 + $rate * $type) * $nper + $fv;
    } else {
        $f = exp($nper * log(1 + $rate));
        $y = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;
    }
    $y0 = $pv + $pmt * $nper + $fv;
    $y1 = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;

    // find root by secant method
    $i  = $x0 = 0.0;
    $x1 = $rate;
    while ((abs($y0 - $y1) > FINANCIAL_PRECISION) && ($i < FINANCIAL_MAX_ITERATIONS)) {
        $rate = ($y1 * $x0 - $y0 * $x1) / ($y1 - $y0);
        $x0 = $x1;
        $x1 = $rate;

        if (abs($rate) < FINANCIAL_PRECISION) {
            $y = $pv * (1 + $nper * $rate) + $pmt * (1 + $rate * $type) * $nper + $fv;
        } else {
            $f = exp($nper * log(1 + $rate));
            $y = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;
        }

        $y0 = $y1;
        $y1 = $y;
        ++$i;
    }
    return $rate;
}   //  function RATE()

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