MAT-144 · Mathematical Reasoning
Topic 04 · Loans
Vocabulary & key terms
Every term defined across this topic, grouped by lesson. Tap a lesson title to jump back to the page where the term was introduced.
31
terms in this topic. Skim before the review.
Course tool
All seven ALEKS dictionary formulas in one calculator — including the loan amortization monthly-payment formula. Solve for any variable; Excel workbook included.
- 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.
- Loan amortization formula
- The expression above. The only formula in the ALEKS dictionary not introduced in T3.
- Periodic rate (r/12)
- The monthly interest rate. Annual rate divided by 12 because there are 12 monthly compounding periods per year.
- Total payments (12t)
- The total number of monthly payments over the life of the loan. A 5-year auto loan has 60 payments; a 30-year mortgage has 360.
- Negative exponent
- (1 + r/12)−12t = 1 / (1 + r/12)12t. Most calculators handle the minus sign correctly; in Excel the syntax is
^(-12*t). - Total cost / total interest
- Total cost of a loan = M × 12 × t (every payment summed). Total interest = total cost − principal. Both grow fast as t increases.
- Auto loan
- A fixed-term loan to buy a vehicle. Term typically 3-7 years; rate depends on credit score and current rates.
- Down payment
- Money paid up front. Reduces the principal you finance and the monthly payment that results. Usually 10-20% of sticker price.
- Sticker price (total cost)
- The full price of the vehicle. Equals down payment plus the loan amount.
- Amount financed (P)
- The principal of the loan. Sticker price minus down payment. This is the P that goes into the amortization formula.
- Term length
- The loan duration in years. Longer term means lower monthly payment but more total interest paid.
- Revolving credit
- A loan with no fixed term — you can borrow more, pay down, repeat. Credit cards and home-equity lines of credit are the common examples.
- APR (credit card)
- The annual rate the card charges on unpaid balances. Typical range: 18-29%. Divide by 12 for the monthly periodic rate.
- Minimum payment
- The smallest payment the card issuer requires each month. Usually 1-3% of balance, plus the interest charged that month. Pays the loan off agonizingly slowly.
- Interest portion
- The part of your payment that covers the month's interest charge. Computed first; what's left goes to principal.
- Principal portion
- The part of your payment that actually reduces the balance. Equals payment − interest portion.
- Subsidized loan
- Federal loan where the government pays interest during in-school years and deferment. Only available to students with demonstrated financial need.
- Unsubsidized loan
- Federal loan where interest accrues from disbursement. Available regardless of need.
- Capitalization
- Accrued in-school interest gets added to the principal at the start of repayment, increasing the amount you'll pay back. ALEKS uses simple interest (I = Prt) for the in-school accrual; real federal loans accrue daily.
- Deferment
- A pause in repayment (e.g. while in school). Subsidized loans don't accrue interest during deferment; unsubsidized loans do.
- Standard vs Income-Driven Repayment
- Standard: 10-year fixed term, computed by the L2 formula. IBR (income-driven): monthly payment is a percent of discretionary income, term up to 25 years, with possible forgiveness of remaining balance.
- Mortgage
- A long-term loan secured by real estate. Standard terms are 15 or 30 years; the home itself is collateral.
- Principal/interest split
- How each monthly payment breaks down. Front-loaded toward interest in early years, back-loaded toward principal in later years.
- Amortization schedule
- A row-by-row table of every payment, the interest portion, the principal portion, and the remaining balance. The full visual record of how the loan gets paid off.
- Escrow
- An account the lender holds to pay your property taxes and homeowner's insurance. You pay 1/12 of the annual amount each month as part of your mortgage payment.
- PITI
- Principal + Interest + Taxes + Insurance — the four components of a typical mortgage payment. When people say "my mortgage" they usually mean PITI.
- Refinancing
- Replacing an existing mortgage with a new one, usually at a lower rate. Resets the amortization clock.