What a loan is, and what amortization means.
Before any formula: four pieces (P, r, t, M) and a concept (amortization). A loan is principal you pay back in fixed monthly chunks; each chunk is part interest, part principal, until the principal hits zero.
You walk into a dealership. The salesperson points at a $25,000 car and says "just $483 a month for 60 months." Sounds reasonable. Quick math:
$483 × 60 = $28,980
You're paying $3,980 over the sticker price. That's the interest the bank charges for letting you spread the payment across five years instead of writing one $25,000 check today. That $3,980 doesn't appear on the price tag; it's hiding inside the monthly number.
This whole topic is about doing that math out loud — for auto loans, credit cards, student loans, and mortgages. Lesson 1 names the pieces. Lesson 2 gives you the formula that produces the $483 in the first place. By the end of the topic, you'll never trust a monthly number on its own again.
A loan trades a lump sum now for a stream of payments later.
Three pieces every loan has. The principal you borrowed on day one (left), the stream of monthly payments in between (middle), and the total you'll actually pay over the life of the loan (right). The gap between the two big numbers is interest.
Amortization is the process of paying off a loan through scheduled equal payments, with each payment covering the period's interest first and reducing the principal with whatever is left over.
The four names you need (and one verb)
- Principal (P) The amount you borrowed — the loan amount. Sticker price minus any down payment.
- Annual rate (r) The annual interest rate as a decimal. 6.5% becomes 0.065. The amortization formula uses r/12 internally to convert to a monthly periodic rate.
- Term (t) The length of the loan in years. Auto loans are usually 3-7; mortgages are 15 or 30; credit cards have no fixed term.
- Monthly payment (M) The fixed amount you pay each month. The amortization formula in Lesson 2 computes this from the other three pieces.
- Amortize To pay off a loan in fixed payments over time. Each payment is interest first, principal second.
Maria's auto loan: name every piece.
"Maria buys a $30,000 car. She makes a $5,000 down payment and finances the rest with a 5-year loan at 6% APR. The bank tells her the monthly payment is $483.32. What's the total cost of the car including interest?"
Identify the principal P (loan amount).
The sticker price is $30,000, but the loan only finances what's left after the down payment.
Identify rate, term, monthly payment.
r = 0.06 (6% as a decimal). t = 5 (years). M = $483.32 (given by the bank — Lesson 2's formula will produce this from P, r, and t).
Compute total paid.
Total paid = monthly payment × number of months. 5 years × 12 months/year = 60 monthly payments.
Compute total interest.
Total interest = total paid − loan amount. Note: this is interest on the amount financed, not the sticker price. Maria's $5,000 down payment didn't earn the bank any interest.
Compute total cost of the car.
This is what most people don't compute: the full out-of-pocket cost including the down payment and all 60 monthly payments.
Three problems. Different missing pieces. Same recipe.
A car has a sticker price of $35,000. The buyer puts 12% down. What's the loan amount (the principal P)?
A loan has monthly payment M = $425 over a 5-year term. What's the total amount paid over the life of the loan?
A $22,000 loan is paid off with monthly payments of $425 over 5 years. How much total interest is paid?
Three fast questions before you move on.
Q1. The variable P in a loan formula is...
Q2. Amortization is best described as...
Q3. If you stretch a loan from 5 years to 7 years at the same rate, the monthly payment will decrease, but the total interest paid will...
Naming the pieces, then the formula.
Every loan in this topic uses the same four pieces. Once you can identify P, r, t for any loan, M falls out of one formula. Auto loans, mortgages, student loans — they're all variations on the same skeleton.
Next: Lesson 2 introduces the formula of Topic 4 — the loan amortization formula. It looks intimidating at first; after one worked example it's just another recipe.
Continue to Lesson 02Different angle? Need another rep? These are optional — tap any that look helpful.
Amortization schedules and time to pay off
A concise intro to amortization with a worked schedule. Defines principal, interest, payment, and how each payment splits between the two.
How Cars Keep You POOR!
Accessible 5-minute intro to how a consumer loan actually works, using a car as the concrete example. A great hook before the formula in Lesson 4.2.