首期到底係幾多?

A=monthly payment (i.e. $5,000)
r = interest (i.e. 4%/12 = 1/300)
n = number of instalment (i.e.25*12 = 300)
Po=principal: to be calculated

A = [Po * r * (1+r) ^n] / [(1+r) ^n-1]

5,000 = [Po /300 * (1+1/300) ^ 300] / [(1+1/300) ^ 300 – 1]
[Po /300 * (1+1/300) ^ 300] = 8,568.8257
Po * 0.009046 = 8,568.8257
Po = 947,250

$1,080,000萬單位，借款本金為$947,250，所以首期
= $1,080,000 - $947,250
= $132,750

Assuming the interest is annual at 4%,
then if
R=rate(4里息)=1+4%=1.04
I=installment per annum(月供x12)=5000*12=60000
P=principal (after 首期)
n=number of periods(年)=25

PR^n=I*(R^n-1)/(R-1)
P=I(R^n-1)/R^n/(R-1)
=60000(1.04^25-1)/(1.04^25)/(1.04-1)
=937324.80

The downpayment (首期) is therefore
1080000-937324.8
=$142,675.20