Methodology: how we calculate every result

We think a finance tool should show its work. Every calculator on this site uses standard, published financial formulas — no black boxes and no fudge factors. Here is exactly what runs behind each one, so you can trust the output and check it yourself.

Loan Calculator

M = P × r ÷ (1 − (1 + r)^−n)

We use the standard amortization formula, where P is the amount borrowed, r is the monthly rate (the annual interest rate ÷ 12 ÷ 100), and n is the number of monthly payments. We ask for the annual interest rate — the note rate — not the fee-inclusive APR, because the rate alone determines the payment. The schedule is built month by month: each payment is split into interest (balance × r) and principal (the remainder), and the balance is reduced accordingly. Extra payments are applied straight to principal, which shortens the term and lowers total interest. The final payment is capped at the remaining balance plus its interest so the loan never overpays.

Compound Interest Calculator

balance = balance × (1 + r) + contribution, each month

We convert your nominal annual rate at the chosen compounding frequency into an equivalent monthly rate — r = (1 + annual rate ÷ f)^(f ÷ 12) − 1 — then step the balance forward one month at a time, applying that month's growth and then adding your contribution. This handles monthly, quarterly, or annual compounding with a single consistent method. "Interest earned" is the final balance minus everything you contributed.

Savings Goal Planner

r = (1 + APY)^(1 ÷ 12) − 1

We turn your APY into a monthly growth rate, then step the balance forward one month at a time: we apply that month's growth first and then add your deposit (so deposits are treated as end-of-month contributions), repeating until the balance reaches your goal — that is your timeline. For the deadline mode, we invert the future-value-of-an-annuity formula (ordinary annuity, matching the end-of-month timing) to solve for the exact monthly deposit needed: PMT = (FV − PV × (1+r)^n) × r ÷ ((1+r)^n − 1). Savings accounts are quoted as APY, so that is the input we ask for here.

Debt Payoff Calculator

snowball → smallest balance first | avalanche → highest APR first

We simulate payoff month by month. Interest accrues on every balance (balance × APR ÷ 12), every debt receives its minimum, and all remaining budget is funnelled into one target debt chosen by the strategy. Credit cards and other revolving debt are quoted as APR, so APR is the correct input here. When a debt clears, its payment rolls into the next target — the "snowball" effect. We run both strategies on your real numbers so you can compare payoff dates and total interest side by side.

Rent vs. Buy Calculator

compare net worth, same starting cash, same monthly budget

This is the comparison most tools get wrong. Both parties start with the same cash (the buyer's down payment plus closing costs) and spend the same total on housing each month; whoever spends less on housing invests the difference at your investment-return rate. We then compare each path's net worth — the buyer's home equity (sale value net of selling costs, minus the remaining loan) plus side investments, versus the renter's portfolio. The model includes buying closing costs, selling costs, annual appreciation, rent growth, and a yearly tax-insurance-upkeep percentage. Because the starting cash and monthly outlay are identical, neither side is rigged to win.

Retirement Calculator

nest egg via monthly compounding; income ≈ nest egg × 4%

We project your nest egg with the same monthly compounding engine as the compound calculator: your current savings grow at your expected annual return (converted to a monthly rate), with your monthly contribution added each month from now until your retirement age (years = retirement age − current age). We then apply the "4% rule" — a common rule of thumb — to estimate a first-year retirement income of about 4% of the balance, and one-twelfth of that per month. The 4% rule is a guideline, not a guarantee: real safe-withdrawal rates depend on markets, fees, how long you live, and how flexible you can be in down years. Returns are assumed constant and are not inflation-adjusted.

Auto Loan Calculator

financed = price − down − trade-in + sales tax; then amortize

We first work out the amount actually financed: the vehicle price minus your down payment and trade-in, plus any sales tax you choose to enter. That figure is amortized with the same standard loan formula, at your annual interest rate ÷ 12, over the term in months. Total interest is the sum of payments minus the amount financed. The sales-tax field is optional; when you use it, the tax is added to the financed balance (financed alongside the car) rather than treated as a separate upfront cost.

Refinance Calculator

break-even (months) = closing costs ÷ monthly saving

We amortize both loans with the standard formula — your current loan over its remaining years, and the proposed loan over its new term — using each loan's annual interest rate (the note rate, not APR). The monthly saving is your current payment minus the new payment; the break-even month is your closing costs divided by that saving, rounded up. We also compare lifetime interest — your current loan's remaining interest versus the new loan's total interest plus closing costs — so a lower rate that restarts the clock on a longer term cannot look cheaper than it really is.

Net Worth Calculator

net worth = total assets − total liabilities

We sum every asset line and every liability line you enter, then subtract total liabilities from total assets. There are no rate or time assumptions — it is a straight snapshot of what you own minus what you owe. We suggest entering your home at its market value as an asset and the remaining mortgage as a separate liability, rather than as net equity, so both sides of your balance sheet stay visible.

Debt-to-Income Calculator

front-end = housing ÷ income; back-end = (housing + other debt) ÷ income

We divide your monthly housing payment by your gross monthly income for the front-end (housing) ratio, and your total monthly debt — housing plus other debt payments — by gross income for the back-end ratio. Both are shown as percentages and compared against the 28/36 rule lenders commonly use. "Gross" means before-tax income, which is the figure lenders evaluate; this tool takes the payment amounts you already know, so it makes no rate or amortization assumptions of its own.

What our numbers exclude

Our results are clean models, which means each tool deliberately leaves out things that vary too much to assume for you — most often income and capital-gains taxes, mortgage insurance (PMI), HOA dues, and the tax deductibility of mortgage interest where it applies. There are deliberate exceptions, because some real costs are inputs: the auto loan calculator can add sales tax to the financed amount, the refinance calculator takes your closing costs, and the rent vs. buy calculator includes buying closing costs, selling costs, and a yearly tax-insurance-upkeep percentage. Where a specific cost is not an input, we call it out on the tool it affects. Treat every result as a well-founded estimate, not a quote.

Editorial standards

Our guides explain the same math our calculators run — not outsourced or auto-generated filler. Every worked example is calculated with the standard formulas the tools use (the amortization formula for loans, effective-rate compounding for savings) and checked against those calculators. Automated tests check the calculators’ outputs and selected published examples against known-correct values, so those figures stay in sync with the tools. We revise guides when the math, the figures, or best practice changes, and note the last-reviewed date on each. This is educational information, not personalized financial advice.

Content is written and reviewed by SmartMoney Tools. When we cite a rule of thumb — the 28/36 rule, the 50/30/20 budget, the three-to-six-month emergency fund — we explain where it comes from and when it does and does not apply, rather than presenting it as gospel.

Found something that looks off?

We take accuracy seriously. If a result does not match your own math, tell us and we will look into it.