Mortgage & Amortization Calculator
PITI + PMI monthly payment with the live 30-year principal-vs-interest curve.
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$
20% down · No PMI
%
yr
%
$/yr
Monthly payment (PITI + PMI)
$2,505.95
P&I $2,022.62 · Tax $366.67 · Ins $116.67
Loan principal
$320,000.00
$80,000.00 down on $400,000.00
Total interest
$408,142.36
127.5% of principal
Total of payments
$728,142.36
30 × 12 P&I payments
Cumulative principal vs interest paid
Mortgage — answers & formulas
Deep-dive formulas, definitions, and worked examples — indexed for search and ready to share.
Math HistoryFrance · 1642
The 17th-Century Tax Crisis
An 18-year-old French math prodigy named Blaise Pascal grew tired of watching his father labor over grueling, manual tax bookkeeping. To solve the problem, he invented the Pascaline—the world's first operational mechanical calculator. It executed addition and subtraction using a complex internal system of interlocking clock gears and brass wheels, hand-turned via a metal stylus.
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