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
= 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
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