Loans & Interest Rates
A loan is borrowed money you repay over time, plus interest — the price the lender charges for the use of their money.
The three numbers that define a loan
Principal — how much you borrowed.
Interest rate — the % the lender charges. Stated as APR for most loans.
Term — how long you have to pay it back. Shorter term = higher monthly payment, far less total interest.
APR vs APY
APR (Annual Percentage Rate) — what loans use. Includes interest plus most upfront fees, but doesn't compound the rate.
APY / EAR (Annual Percentage Yield / Effective Annual Rate) — what savings/investments use. Compounds the rate. Always ≥ APR for the same nominal rate.
The amortization formula
M = P · [ r·(1+r)n / ((1+r)n − 1) ]M monthly payment · P principal · r periodic (monthly) rate · n number of payments. Every payment is the same amount, but the split between interest and principal shifts over time.
Interactive loan calculator
| # | Payment | Interest | Principal | Balance |
|---|
Loan types at a glance
Mortgage
Long-term loan to buy a home. Usually 15 or 30 years, fixed or adjustable rate. Interest is often tax-deductible if you itemize.
Secured by the homeAuto loan
3–7 years. Vehicles depreciate fast — long terms (72+ mo) often leave you "underwater" (owing more than the car is worth).
Secured by the vehicleStudent loan
Federal loans have flexible repayment plans, deferment, and forgiveness options. Private loans usually don't.
UnsecuredPersonal loan
Fixed-term, fixed-payment loans for debt consolidation, big purchases, etc. Rate driven heavily by credit score.
Usually unsecuredCredit cards
Revolving credit. Pay in full → free borrowing. Carry a balance → among the most expensive consumer debt available.
Unsecured · variable rateHELOC / Home equity
Borrow against your home equity. Usually variable rate. Cheaper than personal loans, but your house is the collateral.
Secured by the homeSmart-borrowing checklist
- Shop at least 3 lenders. Mortgage/auto inquiries within ~30 days count as one for credit-score purposes.
- Compare APR, not just the "rate" — APR includes most fees and gives a true cost picture.
- Shorter terms cost less in total interest. A 15-yr mortgage often pays less than HALF the interest of a 30-yr.
- Avoid prepayment penalties — many states ban them, but check the loan documents.
- Watch for "teaser" rates and adjustable-rate triggers, especially on credit cards and ARMs.
- Never borrow to invest in speculative assets. The math rarely works once volatility is included.
30-yr fixed mortgage rate — recent history
US average 30-yr fixed mortgage rate, year-end (rough). Source: Freddie Mac PMMS data.
Connect the dots
Quiz
15 questions on loans, rates and amortization.
Flashcards
Tap to flip. Key loan & interest terms.
Teacher mode
Lesson outline, quick reference, and a printable worksheet with answer key.
Lesson outline (40 min)
- 5 min · Hook — Plug $300k, 6%, 30 yr into the calculator. Reveal total interest paid (>$340k). Compare to 15-yr term.
- 10 min · Amortization concept — Show how each payment is the same dollar amount but the interest/principal mix flips over the life of the loan.
- 10 min · Loan types — Walk through the comparison cards. Discuss secured vs unsecured and typical rate ranges.
- 10 min · "Extra principal" demo — Add $200/mo to a 30-yr mortgage. Watch payoff time drop ~7 years and total interest fall by ~$70k.
- 5 min · Wrap — Quick-fire: APR vs APY · why same rate compounded daily yields more · why credit-card minimums are a trap.