This technical guide outlines the mathematical architecture
powering the calculator. Formulas are rendered in professional
financial notation formats.
1. Down Payment & Financed Principal Amount
D =
Vsale ×
(
Ppct
100
)
[Percentage Mode]
D =
Vfixed
[Fixed Dollar Mode]
P =
Vsale −
D
Where Vsale represents the home purchase
price, D is total equity down
payment, and P is the net financed
principal loan balance.
2. Discount Points Upfront Cost & Interest Rate Impact
Cpoints =
P ×
Npaid ×
(
Cper_point
100
)
Reffective =
Rbase −
(
Npaid × ΔRper_point
)
Where Npaid is the quantity of interest
rate reduction points bought, and Cpoints is the additional cash
requirement at closing.
3. Scheduled Monthly Amortization Formula (M) & Break-Even Analysis
r =
R / 100
k
,
n =
t ×
k
M =
P ×
[
r(1 +
r)n
(1 + r)n
− 1
]
ΔM =
Mbaseline −
Meffective
Where k represents payments per
year (12), t is total term years,
M is the periodic installment, and
Tbreakeven is the time required to
recoup upfront costs in months.
4. Non-Principal Fixed Escrow Charges
Mescrow =
(
Atax +
Ains +
Apmi +
Ahoa
k
)
Aggregates recurring monthly fees where
A values represent annual tax
appraisals, homeowner insurance policies, private mortgage
insurance, and HOA dues.
5. Progressive Amortization Ledger Recurrence Relation (Period
t)
It =
Bt−1 ×
r
Pt = min(M −
It ,
Bt−1)
Et = min(Mextra +
Mrow_custom ,
Bt−1 −
Pt)
Bt =
Bt−1 −
Pt −
Et
Where Bt−1 is the previous row's ending
principal balance, It is monthly accrued interest,
Pt is scheduled equity paydown,
and Bt is the resulting ending
balance.