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Mortgage Basics & Calculations Cheat Sheet
A printable reference covering mortgage payments, principal, interest, down payments, escrow, amortization, and closing costs for grades 11-12.
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This cheat sheet covers the basic terms and calculations used when buying a home with a mortgage. Students need these skills to understand loan offers, compare monthly payments, and estimate the true cost of borrowing. Mortgage math connects percentages, exponents, budgeting, and long-term financial planning. It also helps students recognize how small changes in rates or loan length can create large differences in total cost. The core ideas are principal, interest rate, loan term, monthly payment, escrow, and amortization. The standard fixed-rate mortgage payment formula is M = P[r(1 + r)^n] / [(1 + r)^n - 1], where P is the loan amount, r is the monthly interest rate, and n is the number of monthly payments. Total paid equals monthly payment times number of payments, and total interest equals total paid minus principal. A complete housing budget should also include property taxes, homeowners insurance, possible PMI, HOA fees, maintenance, and closing costs.
Key Facts
- Loan amount equals home price minus down payment, so P = price - down payment.
- Monthly interest rate equals annual interest rate divided by 12, so r = APR / 12 when APR is written as a decimal.
- Number of payments equals years times 12, so n = loan term in years x 12.
- For a fixed-rate mortgage, the monthly principal and interest payment is M = P[r(1 + r)^n] / [(1 + r)^n - 1].
- Total paid over the loan equals M x n, and total interest equals total paid - P.
- A larger down payment lowers the loan amount and may help the buyer avoid private mortgage insurance.
- Escrow payments usually include property taxes and homeowners insurance, so monthly housing cost is more than principal and interest.
- Closing costs are often about 2% to 6% of the home price and are paid at closing unless rolled into the loan.
Vocabulary
- Mortgage
- A loan used to buy real estate, with the property serving as collateral for the lender.
- Principal
- The amount of money borrowed or the remaining loan balance before interest is added.
- Interest
- The cost of borrowing money, usually shown as a yearly percentage rate.
- Amortization
- The process of paying off a loan through scheduled payments that gradually reduce the principal balance.
- Escrow
- An account used by the lender to collect and pay costs such as property taxes and homeowners insurance.
- Private Mortgage Insurance
- Insurance often required when the down payment is less than 20%, protecting the lender if the borrower defaults.
Common Mistakes to Avoid
- Using the annual interest rate directly in the monthly payment formula is wrong because the formula requires the monthly rate, r = APR / 12.
- Forgetting to convert the loan term into months is wrong because a 30-year mortgage has n = 30 x 12 = 360 payments, not 30 payments.
- Comparing only monthly payments is misleading because a longer loan may have a lower payment but much higher total interest.
- Ignoring taxes, insurance, PMI, and HOA fees gives an unrealistically low housing budget because principal and interest are only part of the monthly cost.
- Treating the down payment as the only upfront cost is incorrect because buyers often also need closing costs, moving costs, and emergency savings.
Practice Questions
- 1 A home costs $320,000 and the buyer makes a 10% down payment. What is the loan amount?
- 2 A borrower takes a $250,000 fixed-rate mortgage at 6% annual interest for 30 years. Using r = 0.06 / 12 and n = 360, estimate the monthly principal and interest payment with M = P[r(1 + r)^n] / [(1 + r)^n - 1].
- 3 A mortgage payment for principal and interest is 275,000 loan. What is the total paid, and how much is total interest?
- 4 Explain why a buyer should compare total interest, escrow costs, and closing costs instead of choosing a mortgage only by the lowest monthly payment.