/**
 * Core financial functions replicating Excel's PMT, IPMT, PPMT.
 * All functions return positive values (Excel returns negative for payments).
 */

/**
 * PMT — Fixed periodic payment for a loan.
 * Equivalent to Excel: -PMT(rate, nper, pv)
 */
export function pmt(rate: number, nper: number, pv: number): number {
  if (pv <= 0 || nper <= 0) return 0;
  if (rate === 0) return pv / nper;
  const factor = Math.pow(1 + rate, nper);
  return (pv * rate * factor) / (factor - 1);
}

/**
 * IPMT — Interest portion of a specific payment period.
 * Equivalent to Excel: -IPMT(rate, per, nper, pv)
 * @param per 1-based period number
 */
export function ipmt(rate: number, per: number, nper: number, pv: number): number {
  if (rate === 0 || pv <= 0 || nper <= 0) return 0;
  const bal = remainingBalance(rate, per - 1, nper, pv);
  return bal * rate;
}

/**
 * PPMT — Principal portion of a specific payment period.
 * Equivalent to Excel: -PPMT(rate, per, nper, pv)
 * @param per 1-based period number
 */
export function ppmt(rate: number, per: number, nper: number, pv: number): number {
  if (pv <= 0 || nper <= 0) return 0;
  return pmt(rate, nper, pv) - ipmt(rate, per, nper, pv);
}

/**
 * Remaining balance after `per` payments.
 * @param per Number of payments already made (0 = initial balance)
 */
export function remainingBalance(rate: number, per: number, nper: number, pv: number): number {
  if (pv <= 0 || nper <= 0) return 0;
  if (per <= 0) return pv;
  if (per >= nper) return 0;

  if (rate === 0) {
    return pv - pmt(rate, nper, pv) * per;
  }

  const payment = pmt(rate, nper, pv);
  const factor = Math.pow(1 + rate, per);
  return pv * factor - payment * (factor - 1) / rate;
}