Question

考虑到初始贷款金额，还款数量和还款金额，我正在尝试计算贷款利息。我似乎无法使用基本公式获得足够接近的数字，所以我一直在尝试使用Newton Raphson方法，这可以在这里使用：http://www.efunda.com/formulae/finance/loan_calculator.cfm（这是我的确切功能希望实施）

我已经尝试过使用PHPExcel的RATE（）函数，但是我没有为输入获得正确的输出，即利率回到0.1％或类似（实际上它更像是5.75％）

这是PHPExcel的相关代码

/** FINANCIAL_MAX_ITERATIONS */
define('FINANCIAL_MAX_ITERATIONS', 128);

/** FINANCIAL_PRECISION */
define('FINANCIAL_PRECISION', 1.0e-08);

/**
 * Convert an array to a single scalar value by extracting the first element
 *
 * @param   mixed       $value      Array or scalar value
 * @return  mixed
 */
function flattenSingleValue($value = '') {
    while (is_array($value)) {
        $value = array_pop($value);
    }

    return $value;
}

/**
 * RATE
 *
 * Returns the interest rate per period of an annuity.
 * RATE is calculated by iteration and can have zero or more solutions.
 * If the successive results of RATE do not converge to within 0.0000001 after 20 iterations,
 * RATE returns the #NUM! error value.
 *
 * Excel Function:
 *      RATE(nper,pmt,pv[,fv[,type[,guess]]])
 *
 * @access  public
 * @category Financial Functions
 * @param   float   nper        The total number of payment periods in an annuity.
 * @param   float   pmt         The payment made each period and cannot change over the life
 *                                  of the annuity.
 *                              Typically, pmt includes principal and interest but no other
 *                                  fees or taxes.
 * @param   float   pv          The present value - the total amount that a series of future
 *                                  payments is worth now.
 * @param   float   fv          The future value, or a cash balance you want to attain after
 *                                  the last payment is made. If fv is omitted, it is assumed
 *                                  to be 0 (the future value of a loan, for example, is 0).
 * @param   integer type        A number 0 or 1 and indicates when payments are due:
 *                                      0 or omitted    At the end of the period.
 *                                      1               At the beginning of the period.
 * @param   float   guess       Your guess for what the rate will be.
 *                                  If you omit guess, it is assumed to be 10 percent.
 * @return  float
 **/
function RATE($nper, $pmt, $pv, $fv = 0.0, $type = 0, $guess = 0.1) {
    $nper   = (int) flattenSingleValue($nper);
    $pmt    = flattenSingleValue($pmt);
    $pv     = flattenSingleValue($pv);
    $fv     = (is_null($fv))    ? 0.0   :   flattenSingleValue($fv);
    $type   = (is_null($type))  ? 0     :   (int) flattenSingleValue($type);
    $guess  = (is_null($guess)) ? 0.1   :   flattenSingleValue($guess);

    $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 = $rate;
        if (($nper * abs($pmt)) > ($pv - $fv))

            $x1 = abs($x1);

        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()

我对该功能的输入是：

RATE(60, 1100, 50000);     // Outputs 0.00420298759161

RATE(60, -1100, 50000);    // Outputs 0.00959560344752

RATE(60, 1100, 66000);     // Outputs -1.05036370955

如果60是5年的月数，则1100或-1100是每月偿还的金额，50,000是借款总额。

我不是数学家，上面的函数对我来说没有多大意义，但我的阅读说这是计算速率的最佳方法。希望我只是犯了一个愚蠢的错误......

Answer 1

您可以使用“二进制搜索”代替“Newton Raphson方法”。

function rate($month, $payment, $amount)
{
    // make an initial guess
    $error = 0.0000001; $high = 1.00; $low = 0.00;
    $rate = (2.0 * ($month * $payment - $amount)) / ($amount * $month);

    while(true) {
        // check for error margin
        $calc = pow(1 + $rate, $month);
        $calc = ($rate * $calc) / ($calc - 1.0);
        $calc -= $payment / $amount;

        if ($calc > $error) {
            // guess too high, lower the guess
            $high = $rate;
            $rate = ($high + $low) / 2;
        } elseif ($calc < -$error) {
            // guess too low, higher the guess
            $low = $rate;
            $rate = ($high + $low) / 2;
        } else {
            // acceptable guess
            break;
        }
    }

    return $rate * 12;
}

var_dump(rate(60, 1000, 20000));
// Return 0.56138305664063, which means 56.1383%

“二元搜索”和“牛顿拉斐逊方法”基本上是一种猜测方法。它会进行初步猜测并随着时间的推移改进猜测，直到达到可接受的猜测。 “Newton Raphson方法”通常比“二分搜索”更快，因为它有更好的“改进猜测”策略。

概念很简单：

enter image description here

我们想知道r哪个是利率。我们知道，N，C和P.我们不知道什么是r，但是让我们猜测0.00到1.00之间的任何数字。（在这种情况下，我们假设利率不能超过100％）。

第1步：随机猜测
第2步：将费率插入公式，
步骤3：检查猜测是否过低，猜测更高，转到步骤2
步骤4：检查猜测是否过高，降低猜测，转到步骤2
第5步：我们得到了可接受的费率。
第6步：r是每月费率。多次乘12来获得年率。

用PHP计算利率

1 个答案: