APR vs APY, explained with numbers
APR is the yearly price of borrowing before compounding; APY is what you actually earn (or pay) after compounding kicks in. A 5% APR compounded monthly is a 5.116% APY — the gap widens as compounding gets more frequent.
Use APR to compare loans and credit cards, APY to compare savings accounts. Mixing them up is how a 'lower rate' ends up costing more: always convert both offers to the same measure before signing.
Common mistakes: ignoring fees (they belong in the APR), comparing monthly-compounded vs daily-compounded rates head-on, and trusting rounded marketing figures. Recompute with the exact nominal rate and frequency.
Example: $10,000 at 5% APR, monthly compounding → APY = (1+0.05/12)^12 − 1 = 5.116%, i.e. $511.62 interest in a year, not $500.
Try: APY Calculator · APR Calculator
How mortgage amortization really works
Every mortgage payment splits into interest (on the remaining balance) and principal (what you truly repay). Early years are mostly interest; the split flips slowly — that schedule is called amortization.
It matters because extra payments attack principal directly and skip future interest. Paying $100 extra monthly on a 30-year loan can shave years off and save five figures in interest.
Mistakes: comparing only the monthly payment (a longer term looks cheaper but costs more), forgetting tax/insurance (PITI), and refinancing without computing the break-even month of closing costs.
Example: $300,000 at 6.5% over 30 years → ~$1,896/mo. An extra $200/mo pays it off ~7 years early and saves ~$90,000 in interest.
Try: Mortgage Payment Calculator · Refinance Calculator
Compound interest: the 3 levers that matter
Compound interest has three levers: how much you put in, the rate of return, and — the most underestimated — time. Returns earn their own returns, so growth is exponential, not linear.
Time beats timing: starting 10 years earlier usually beats saving double later. That is why retirement accounts reward the boring habit of contributing every month from the first paycheck.
Mistakes: chasing return while ignoring fees (a 1% fee compounds against you too), pausing contributions in dips (you miss the recovery compounding), and confusing average return with the compound path.
Example: $500/mo at 7% for 30 years → ~$566,000 (you put in $180,000). The Rule of 72 says money doubles every ~10.3 years at 7%.
Try: Compound Interest Calculator · Rule of 72 Calculator
How credit-card minimums trap you
A credit-card minimum (often ~2% of the balance) is engineered to maximize interest: on a $5,000 balance at 22% APR, minimums stretch repayment past 15 years and more than double what you borrowed.
It matters because the same money sent as a fixed $150/mo clears the debt in about 4 years. The difference is math, not discipline: fixed payments attack principal while minimums shrink with the balance.
Mistakes: paying only the minimum while still charging, ignoring each card's APR (avalanche: kill the highest rate first), and balance-transferring without comparing the fee against interest saved.
Example: $5,000 at 22% → minimums ≈ $9,500 interest over 16 years; $200/mo fixed ≈ $2,100 interest over 30 months. Run both in the payoff calculator.
Try: Credit Card Interest Calculator · Debt Payoff Calculator (Avalanche)
Refinance break-even, computed
Refinancing swaps your rate for closing costs: the only question is the break-even month — closing costs divided by monthly savings. Everything after that month is profit.
It matters because a lower rate that takes 6 years to break even is a bad deal if you move in 3. Term resets matter too: a new 30-year loan restarts the amortization clock.
Mistakes: comparing rates without costs, ignoring how long you will stay, and cash-out refis that turn equity back into 30 years of interest.
Example: $4,000 costs saving $120/mo → 34 months to break even. Staying 10 years nets about $10,400; moving in year 2 loses about $1,120.
Try: Refinance Calculator · Mortgage Payment Calculator