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Economics & Personal Finance
How a Mortgage Works, Principal, Interest, Amortization
Monthly payments and the amortization schedule
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A mortgage is a long-term loan used to buy a home, where the home itself acts as collateral for the lender. Each monthly payment is usually split between paying back the borrowed amount, called principal, and paying the lender for the cost of borrowing, called interest. Understanding this split matters because it affects how quickly a homeowner builds equity and how much the home ultimately costs. Even a small change in interest rate or loan term can change the total amount paid by thousands of dollars.
Key Facts
- Principal is the original loan balance that must be repaid.
- Interest is the cost of borrowing money, usually stated as an annual percentage rate.
- Monthly interest rate = annual interest rate / 12.
- Monthly payment formula: M = P[r(1 + r)^n] / [(1 + r)^n - 1], where P is principal, r is monthly interest rate, and n is total number of payments.
- Interest portion of a payment = current loan balance × monthly interest rate.
- Equity = home value - remaining mortgage balance.
Vocabulary
- Mortgage
- A mortgage is a loan used to buy real estate, with the property serving as collateral for the lender.
- Principal
- Principal is the amount of money borrowed that still needs to be repaid.
- Interest
- Interest is the fee paid to the lender for using borrowed money.
- Amortization
- Amortization is the process of paying off a loan through scheduled payments that gradually reduce the balance.
- Equity
- Equity is the part of a home's value that the owner truly owns after subtracting the remaining mortgage debt.
Common Mistakes to Avoid
- Confusing the monthly payment with the amount of principal paid is wrong because early mortgage payments are mostly interest, not principal reduction.
- Using the annual interest rate directly in the monthly payment formula is wrong because mortgage payments are monthly, so the annual rate must be divided by 12.
- Assuming a 30-year mortgage costs only the home price is wrong because interest can add a large amount to the total paid over the life of the loan.
- Ignoring loan term when comparing mortgages is wrong because a lower monthly payment over a longer term can still mean much more total interest.
Practice Questions
- 1 A homeowner has a mortgage balance of $240,000 and an annual interest rate of 6%. What is the interest portion of the next monthly payment?
- 2 A 1,800. If the first month's interest is $1,250, how much principal is paid in the first month?
- 3 Two borrowers have the same loan amount and interest rate. One chooses a 15-year mortgage and the other chooses a 30-year mortgage. Explain which borrower will usually pay less total interest and why.