舊文：略谈按揭贷款的利息计算

因为p($n) = 0（“付清”），所以：

$mortgage = $loan*$m_rate/(1-(1+$m_rate)**(0-$n));

p($i) = p($i-1)*(1+$m_rate) – $mortgage – $overpay;
p($i+1) = p($)*(1+$m_rate) – $mortgage – $overpay;
p($i+$j) = p($i+$j)*(1+$m_rate) – $mortgage – $overpay;
p($i+$j) = $loan*(1+$m_rate)**($i+$j) – $mortgage*((1+$m_rate)**($i+$j) – 1)/$m_rate – $overpay*((1+$m_rate)**($j+1) – 1)/$m_rate;

可以看出通项公式：

p($k) = $loan*(1+$m_rate)**($k) – $mortgage*((1+$m_rate)**($k) – 1)/$m_rate – $overpay*((1+$m_rate)**($k-$i+1) – 1)/$m_rate;

p($k) = $loan*(1+$m_rate)**($k) – ($mortgage + $overpay)*((1+$m_rate)**($k) – 1)/$m_rate;

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