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<?php namespace PhpOffice\PhpSpreadsheet\Calculation\Financial\CashFlow\Constant\Periodic; use PhpOffice\PhpSpreadsheet\Calculation\Exception; use PhpOffice\PhpSpreadsheet\Calculation\Financial\CashFlow\CashFlowValidations; use PhpOffice\PhpSpreadsheet\Calculation\Financial\Constants as FinancialConstants; use PhpOffice\PhpSpreadsheet\Calculation\Functions; class Interest { private const FINANCIAL_MAX_ITERATIONS = 128; private const FINANCIAL_PRECISION = 1.0e-08; /** * IPMT. * * Returns the interest payment for a given period for an investment based on periodic, constant payments * and a constant interest rate. * * Excel Function: * IPMT(rate,per,nper,pv[,fv][,type]) * * @param mixed $interestRate Interest rate per period * @param mixed $period Period for which we want to find the interest * @param mixed $numberOfPeriods Number of periods * @param mixed $presentValue Present Value * @param mixed $futureValue Future Value * @param mixed $type Payment type: 0 = at the end of each period, 1 = at the beginning of each period * * @return float|string */ public static function payment( $interestRate, $period, $numberOfPeriods, $presentValue, $futureValue = 0, $type = FinancialConstants::PAYMENT_END_OF_PERIOD ) { $interestRate = Functions::flattenSingleValue($interestRate); $period = Functions::flattenSingleValue($period); $numberOfPeriods = Functions::flattenSingleValue($numberOfPeriods); $presentValue = Functions::flattenSingleValue($presentValue); $futureValue = ($futureValue === null) ? 0.0 : Functions::flattenSingleValue($futureValue); $type = ($type === null) ? FinancialConstants::PAYMENT_END_OF_PERIOD : Functions::flattenSingleValue($type); try { $interestRate = CashFlowValidations::validateRate($interestRate); $period = CashFlowValidations::validateInt($period); $numberOfPeriods = CashFlowValidations::validateInt($numberOfPeriods); $presentValue = CashFlowValidations::validatePresentValue($presentValue); $futureValue = CashFlowValidations::validateFutureValue($futureValue); $type = CashFlowValidations::validatePeriodType($type); } catch (Exception $e) { return $e->getMessage(); } // Validate parameters if ($period <= 0 || $period > $numberOfPeriods) { return Functions::NAN(); } // Calculate $interestAndPrincipal = new InterestAndPrincipal( $interestRate, $period, $numberOfPeriods, $presentValue, $futureValue, $type ); return $interestAndPrincipal->interest(); } /** * ISPMT. * * Returns the interest payment for an investment based on an interest rate and a constant payment schedule. * * Excel Function: * =ISPMT(interest_rate, period, number_payments, pv) * * @param mixed $interestRate is the interest rate for the investment * @param mixed $period is the period to calculate the interest rate. It must be betweeen 1 and number_payments. * @param mixed $numberOfPeriods is the number of payments for the annuity * @param mixed $principleRemaining is the loan amount or present value of the payments */ public static function schedulePayment($interestRate, $period, $numberOfPeriods, $principleRemaining) { $interestRate = Functions::flattenSingleValue($interestRate); $period = Functions::flattenSingleValue($period); $numberOfPeriods = Functions::flattenSingleValue($numberOfPeriods); $principleRemaining = Functions::flattenSingleValue($principleRemaining); try { $interestRate = CashFlowValidations::validateRate($interestRate); $period = CashFlowValidations::validateInt($period); $numberOfPeriods = CashFlowValidations::validateInt($numberOfPeriods); $principleRemaining = CashFlowValidations::validateFloat($principleRemaining); } catch (Exception $e) { return $e->getMessage(); } // Validate parameters if ($period <= 0 || $period > $numberOfPeriods) { return Functions::NAN(); } // Return value $returnValue = 0; // Calculate $principlePayment = ($principleRemaining * 1.0) / ($numberOfPeriods * 1.0); for ($i = 0; $i <= $period; ++$i) { $returnValue = $interestRate * $principleRemaining * -1; $principleRemaining -= $principlePayment; // principle needs to be 0 after the last payment, don't let floating point screw it up if ($i == $numberOfPeriods) { $returnValue = 0.0; } } return $returnValue; } /** * 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]]]) * * @param mixed $numberOfPeriods The total number of payment periods in an annuity * @param mixed $payment 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 mixed $presentValue The present value - the total amount that a series of future payments is worth now * @param mixed $futureValue 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 mixed $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 mixed $guess Your guess for what the rate will be. * If you omit guess, it is assumed to be 10 percent. * * @return float|string */ public static function rate( $numberOfPeriods, $payment, $presentValue, $futureValue = 0.0, $type = FinancialConstants::PAYMENT_END_OF_PERIOD, $guess = 0.1 ) { $numberOfPeriods = Functions::flattenSingleValue($numberOfPeriods); $payment = Functions::flattenSingleValue($payment); $presentValue = Functions::flattenSingleValue($presentValue); $futureValue = ($futureValue === null) ? 0.0 : Functions::flattenSingleValue($futureValue); $type = ($type === null) ? FinancialConstants::PAYMENT_END_OF_PERIOD : Functions::flattenSingleValue($type); $guess = ($guess === null) ? 0.1 : Functions::flattenSingleValue($guess); try { $numberOfPeriods = CashFlowValidations::validateInt($numberOfPeriods); $payment = CashFlowValidations::validateFloat($payment); $presentValue = CashFlowValidations::validatePresentValue($presentValue); $futureValue = CashFlowValidations::validateFutureValue($futureValue); $type = CashFlowValidations::validatePeriodType($type); $guess = CashFlowValidations::validateFloat($guess); } catch (Exception $e) { return $e->getMessage(); } $rate = $guess; // rest of code adapted from python/numpy $close = false; $iter = 0; while (!$close && $iter < self::FINANCIAL_MAX_ITERATIONS) { $nextdiff = self::rateNextGuess($rate, $numberOfPeriods, $payment, $presentValue, $futureValue, $type); if (!is_numeric($nextdiff)) { break; } $rate1 = $rate - $nextdiff; $close = abs($rate1 - $rate) < self::FINANCIAL_PRECISION; ++$iter; $rate = $rate1; } return $close ? $rate : Functions::NAN(); } private static function rateNextGuess($rate, $numberOfPeriods, $payment, $presentValue, $futureValue, $type) { if ($rate == 0.0) { return Functions::NAN(); } $tt1 = ($rate + 1) ** $numberOfPeriods; $tt2 = ($rate + 1) ** ($numberOfPeriods - 1); $numerator = $futureValue + $tt1 * $presentValue + $payment * ($tt1 - 1) * ($rate * $type + 1) / $rate; $denominator = $numberOfPeriods * $tt2 * $presentValue - $payment * ($tt1 - 1) * ($rate * $type + 1) / ($rate * $rate) + $numberOfPeriods * $payment * $tt2 * ($rate * $type + 1) / $rate + $payment * ($tt1 - 1) * $type / $rate; if ($denominator == 0) { return Functions::NAN(); } return $numerator / $denominator; } }