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Interest is the cost of borrowing; the effective cost depends on principal, term, compounding frequency, and fees. Small differences in interest rate or term can cost thousands to tens of thousands of dollars over the life of a loan, making rate comparison essential.
Calculate total interest paid on multiple loan scenarios (e.g., $300k mortgage at 3% vs. 6% over 30 years; credit card balances at 18% vs. 24%). Use loan calculators to make the impact concrete.
Monthly payment is the true cost of borrowing; interest rates matter less than payment size; all interest calculations use simple interest; refinancing always saves money.
You already understand compound interest — the way interest accrues on both principal and previously accumulated interest. Borrowing is compound interest running in reverse and against you. When you take a loan, the lender is applying compound interest math to the balance you owe, and every payment you make goes partly to interest first, with the remainder reducing principal. This is amortization: early in a loan, most of your payment covers interest; later, most covers principal. On a 30-year mortgage, you can pay for a decade and still owe nearly the full original balance, because those payments were almost entirely interest.
The critical variable is the Annual Percentage Rate (APR), which includes both the stated interest rate and lender fees rolled into a single annual figure — this is the true cost of the loan and the number to compare across lenders. A 6.0% stated rate with $4,000 in origination fees may have an APR of 6.3%, while a 6.2% loan with no fees has a lower APR and costs less overall. The compounding frequency also matters: a 6% annual rate compounded monthly applies 0.5% per month to the current balance, which differs slightly from simple annual compounding. Most consumer loans compound monthly.
Small rate differences compound into enormous dollar differences over time. A $300,000 mortgage at 5% over 30 years totals about $579,000 in payments — $279,000 in interest. At 6%, the same loan totals about $647,000 — $347,000 in interest. One percentage point costs roughly $68,000 over the loan's life. The same logic applies to credit cards, which compound at 20–30% annually: carrying a $5,000 balance at 24% APR and paying only the minimum costs more in interest than the original balance within a few years.
Comparing loans only by monthly payment is the trap lenders exploit. A lower payment can mean a longer term, which means more total interest paid — sometimes dramatically more. The right comparison is total cost: principal plus all interest plus fees over the full term. Refinancing makes mathematical sense when the interest savings over the remaining loan life exceed the closing costs of the new loan — a simple break-even calculation tells you how many months it takes for savings to offset costs, and whether you plan to stay long enough to reach that point.