Excel PMT 函數(年金給付額)公式之證明

PV = PMT + PMT /(1+r) + PMT /(1+r) ^2 + … + PMT/(1+r)^(n-1)
      = PMT(1 + 1/(1+r) + 1/(1+r)^2 + ... + 1/(1+r)^(n-1))
      = PMT * (1-1/(1+r)^n)/r

PMT = PV * r / (1 - 1/(1+r)^n)

範例：

利率1.84 的30 年房貸 5,000,000 元，
每期給付額
PMT = 5,000,000 * (1.84%/12) /(1 - 1/(1+(1.84%/12))^30*12)
         = 5,000,000 *  0.15%/(1-1/(1+0.15%)^360)
         = 5,000,000 *  0.15%/(1-1/(1.0015)^360)
         = 5,000,000 *  0.15%/(1-1/1.7153)
         = 5,000,000 *  0.15%/(1-0.5829)
         = 5,000,000 *  0.15%/0.417
         = 5,000,000 *  0.0035
         = 18,083