What is a Mortgage?
A mortgage is a long-term loan used to purchase real estate, typically a home. The property serves as collateral, and the borrower repays the loan plus interest over 15–30 years in monthly installments.
A mortgage is a home loan secured by the property. Monthly payment M = P[r(1+r)^n]/[(1+r)^n-1], where P is principal, r is monthly rate, and n is total months.
Try it: interactive calculator
Step-by-step worked examples
A $400,000 home with 20% down, 6% annual rate, 30-year mortgage. Monthly payment?
Down payment: $400,000 × 0.2 = $80,000 Principal P = $400,000 − $80,000 = $320,000 Monthly rate r = 6% ÷ 12 = 0.005 Months n = 30 × 12 = 360 M = 320,000 × [0.005(1.005)^360] / [(1.005)^360 − 1] ≈ $1,919
$250,000 mortgage at 4% for 15 years. Find monthly payment.
r = 4% ÷ 12 ≈ 0.00333 n = 15 × 12 = 180 M = 250,000 × [0.00333(1.00333)^180] / [(1.00333)^180 − 1] ≈ $1,849
$500,000 home, 10% down, 5% rate, 30 years. Total interest paid?
Principal P = $500,000 × 0.9 = $450,000 Monthly payment M ≈ $2,415 Total paid: $2,415 × 360 = $869,400 Total interest: $869,400 − $450,000 = $419,400
Flashcards
Quick quiz
Q1.In a 30-year mortgage, where does most of the first payment go?
Q2.What role does the property play in a mortgage?
Q3.A fixed-rate mortgage means…
Q4.Why might someone choose a 15-year mortgage over 30 years?
The full card deck, worked steps and AI-tutor support for “What is a Mortgage?” are in Notek — study by hand before your exam.
Common mistakes
My monthly mortgage payment is just principal and interest. — Correct: It often includes principal, interest, property tax (escrow), and insurance — called PITI.
After paying half the loan, I've paid off half the interest. — Correct: Due to amortization, you've paid ~90% of interest but only ~30% of principal after half the time.
An ARM is always cheaper. — Correct: ARMs start low but rates rise; at reset, monthly payment can spike by hundreds.
Refinancing always saves money. — Correct: Refinancing resets the amortization clock; you pay closing costs and may pay more total interest if the new term is longer.
FAQ
What is a mortgage formula?
M = P[r(1+r)^n]/[(1+r)^n-1]; calculates the fixed monthly payment for a loan.
How is mortgage interest calculated?
The lender multiplies the remaining balance by the monthly rate; as principal decreases, interest shrinks.
What is PMI (Private Mortgage Insurance)?
Insurance that protects the lender if you default; required if your down payment is less than 20%.
Can I pay off my mortgage early?
Yes, most mortgages have no prepayment penalty. Extra payments reduce interest and shorten the term.