Finance & tax · Learn
Start with a worked example, then use your own numbers. Each guide explains the steps, assumptions and limits that matter.
Mortgage calculator ↗
Your mortgage payment is only part of your housing budget
A principal-and-interest estimate is a starting point. Add the property costs that are paid through a lender or separately before deciding what fits your monthly budget.
How much does a larger down payment reduce your mortgage payment?
With an unchanged rate and term, the principal-and-interest payment changes in direct proportion to the amount borrowed. The cash needed to buy the home still requires a separate budget.
Could your budget handle a higher mortgage rate?
Compare several contractual-rate scenarios while holding the other inputs constant. This reveals payment sensitivity without pretending to forecast a country’s future interest rates.
Loan calculator ↗
Does a longer loan term really make borrowing cheaper?
A longer term can make a monthly payment easier to manage while increasing the interest paid over time. Compare the payment and the total cost as separate results.
Interest rate versus APR: which number belongs in a loan calculator?
A contractual borrowing rate determines interest, while a broader annual cost measure may include fees. Using the wrong percentage can make a repayment estimate misleading.
What does one extra loan payment actually change?
An extra payment reduces later interest only when it reduces the balance used for interest calculations. The first two months provide a simple way to inspect that mechanism.
Auto loan calculator ↗
Car price is not always the amount you finance
A down payment, trade-in balance and financed charges can make the loan principal different from the advertised vehicle price. Build a simple funding statement before estimating payments.
A low car payment may hide a final balloon payment
A fully amortizing loan repays principal over its scheduled term. Vehicle finance with a final balloon or purchase option has a different cash-flow pattern and cannot be judged by the monthly bill alone.
Why is an auto-loan payoff quote higher than the remaining principal?
A settlement quote can include interest through a specified date and applicable contractual charges. It is different from the principal balance shown on an earlier statement.
Amortization calculator ↗
How to read the first row of an amortization schedule
A monthly payment does not all reduce the debt. Reconcile opening balance, interest, principal reduction and closing balance to understand what a repayment schedule is showing.
Why can the final loan payment differ from the others?
Rounding a payment for display is not the same as rounding every intermediate balance. A small final adjustment can be necessary even when the loan has no interest.
Why has your loan balance fallen by less than your payments?
Total payments include interest as well as principal. For a home, equity also depends on property value, so it cannot be measured by adding up every mortgage payment you have made.
Payment calculator ↗
Zero-interest instalments: how much should each payment be?
Dividing principal by the number of payments is straightforward only when there is genuinely no interest, financed charge or final balloon. A zero-rate label does not describe every cost.
An implausible monthly payment? Check years versus months first
A term-unit mistake can overwhelm a small rate difference. Establish the payment frequency and convert the duration into the unit requested by the calculator before comparing offers.
How to estimate a loan amount from a monthly payment budget
With the rate, term and interest convention fixed, payment is proportional to principal. One calculation can therefore provide a useful starting point for a budget-based loan estimate.
Income tax calculator ↗
Does entering a higher tax bracket tax all your income at that rate?
Progressive income tax commonly applies different rates to different slices of taxable income. The marginal rate and the average burden are different measurements, and both need a clearly defined income base.
Why payroll withholding differs from your final income tax
Money withheld from wages is a payment toward tax, while annual liability is the amount calculated under the applicable rules. Receiving a refund does not mean that the year’s tax liability was zero.
Comparing income tax across countries: check these inputs first
The same numeric salary is not comparable across currencies, tax years or definitions of income. Establish the calculator’s scope before interpreting a cross-country tax comparison.
Compound interest ↗
Simple versus compound interest: when does the difference appear?
The difference depends on whether interest remains invested and earns further interest. A two-year example makes the mechanism visible without relying on a large long-term projection.
Why two savings accounts labeled 12% can produce different calculations
A nominal annual rate compounded monthly and an effective annual rate are different inputs. Identify the rate basis before deciding how a displayed annual percentage should become a monthly rate.
Beginning or end of the month: does deposit timing matter?
Each deposit earns interest only while it is in the account. The compound calculator assumes end-of-month contributions, which differs from depositing before that month’s interest accrues.
Investment calculator ↗
How much of your investment balance is growth rather than new savings?
A rising account balance can come from contributions as well as investment returns. Separate starting capital, later deposits and modeled growth before interpreting the final amount.
How much can a small annual investment fee change the final balance?
Fees reduce the money left invested and the future growth that money could earn. A useful comparison must say whether its assumed return is before or after charges.
After a 20% loss, why does a 20% gain not break even?
Losses and subsequent gains use different starting balances. A recovery percentage must be calculated from the reduced amount rather than simply reversing the sign of the original loss.
Retirement savings ↗
Starting retirement saving ten years later: what changes each month?
A zero-return comparison reveals the effect of time without depending on uncertain investment growth. It is a useful baseline before building more detailed retirement scenarios.
Will a retirement target stated in today’s money still be enough later?
A future account balance is a nominal amount, while living costs may change. Put the saving target and projected spending on the same price basis before comparing them.
Why a retirement balance is not the same as guaranteed monthly income
Accumulating a sum and drawing from it are different calculations. Spending, investment fluctuations and the length of retirement affect how long a balance can support withdrawals.
Simple interest ↗
Simple interest for half a year: when is the answer not exactly half?
An annual interest rate must be paired with time measured in years. Half a year can be represented as 0.5, but a contract using actual days may produce a different fraction.
Can you calculate a full year of interest after withdrawing some principal?
A constant-principal formula only applies while the balance stays unchanged. Split the timeline at deposits, withdrawals or principal repayments, then calculate each segment separately.
Why a flat-rate interest quote is not a standard loan repayment rate
Simple interest on the original principal and interest on a declining loan balance describe different models. Establish how the quoted rate is applied before using it to estimate instalments.
Inflation calculator ↗
Future cost versus present purchasing power: why inflation gives two answers
One calculation asks how much money a future purchase may require. The other asks what a fixed future amount is worth in today’s purchasing power. Their directions are opposite.
A 4% pay rise with 5% inflation: what happens to purchasing power?
The nominal increase in wages is not the same as the change in what those wages can buy. Compare the wage-growth factor with the price-growth factor for an exact calculation.
When inflation changes each year, is the average rate enough?
Successive price changes compound. A simple arithmetic average of annual rates generally does not reproduce the cumulative change over the whole period.
Salary calculator ↗
Hourly pay to annual salary: why 52 weeks is not always the right input
Hourly rate, paid hours per week and paid weeks per year all affect the estimate. A gross-pay projection does not automatically reproduce an employment contract or take-home pay.
Why average monthly income differs from what arrives on payday
Dividing annual earnings by twelve creates a budgeting average. Weekly, fortnightly and monthly payroll schedules distribute cash differently, so that average is not a prediction of every payslip.
How to compare a part-time offer with a full-time salary
Put paid hours and paid weeks on a consistent basis before comparing gross cash earnings. Benefits, commuting costs and job stability need their own assessment.
Sales tax / VAT / GST ↗
How to remove tax from a tax-inclusive price
A tax rate normally applies to the before-tax amount. To separate tax from an inclusive total, divide by one plus the rate rather than applying the percentage directly to the total.
Discount before tax or tax before discount: what actually matters?
The taxable base depends on the transaction rules. A percentage discount and a single percentage tax commute mathematically, but real promotions do not always permit the same tax treatment.
Why one tax rate cannot always be applied to an entire receipt
A basket containing differently taxed items needs separate tax bases. Multiplying the whole purchase by one item’s rate can overstate or understate the total tax.
Discount calculator ↗
Why 20% off followed by 10% off is not 30% off
Successive discounts apply to an already-reduced price. Adding the percentages exaggerates the saving because the second discount uses a different base.
How to recover the original price from a discounted price
Reverse a discount by dividing by the proportion of price that remains. Adding the same percentage to the sale price generally does not restore the original amount.
Buy two, get one free or 30% off: which offer costs less?
Convert promotions into a unit price for identical goods, then consider whether you need the required quantity. The lowest unit price is not always the lowest useful purchase cost.
Tip & split bill ↗
How to split a restaurant bill after adding a tip
Decide which amount the tip applies to, add the tip to the bill and then divide the total by the number of people. Equal splitting is different from allocating each person’s own purchases.
Does an existing service charge mean you should add another tip?
Read the bill before making an additional calculation. A service charge and a voluntary extra tip are separate entries, and the calculator cannot decide whether another payment is appropriate.
Why individually rounded bill shares do not always add up
An equal split can produce fractions smaller than the currency allows you to pay. Allocate the remainder after rounding rather than assuming everyone’s independently rounded amount will reconcile.
Mortgage payoff calculator ↗
For mortgage overpayments, should you enter the original loan or today’s balance?
An early-payoff comparison starts today. Use outstanding principal and the remaining term rather than the entire amount borrowed when the home was purchased.
Does the timing of a mortgage lump-sum payment matter?
Reducing principal earlier can lower the interest-bearing balance sooner when the rate and repayment rules stay unchanged. Liquidity needs and contractual charges still belong in the comparison.
Will interest savings cover the cost of paying a mortgage off early?
The interest difference displayed by a model is a gross saving. Any actual charges and their timing must be considered before describing the result as a net benefit.
Savings goal calculator ↗
How much should you save each month for a fixed target?
Start by dividing the funding gap at zero interest, then add a supportable growth assumption. An optimistic return should not disguise a monthly saving amount that the budget cannot sustain.
Can a later savings deadline make the monthly deposit manageable?
Extending the deadline gives you more contribution periods. At zero interest, dividing the same gap by different month counts makes the trade-off particularly easy to inspect.
Missed a monthly savings deposit? Recalculate from today’s balance
Once actual deposits differ from the plan, use the real balance and remaining months. Continuing the original contribution may leave a shortfall at the original deadline.
Credit card payoff calculator ↗
Why does credit-card debt barely fall even when you pay every month?
Only the part of a payment remaining after interest reduces principal in the simplified model. A small fixed payment can therefore produce very slow progress.
Why can credit-card daily rates use either 365 or 360?
The annual day-count basis comes from the agreement. It should not be chosen casually from the calendar, because the same annual percentage can produce different daily charges.
Why fixed payments and minimum payments need different payoff models
An issuer’s minimum can change as the balance changes. A fixed-payment projection keeps the same monthly amount, so extending the first month’s minimum indefinitely describes a different strategy.
Profit margin and markup calculator ↗
Margin versus markup: what do a cost of 80 and price of 100 mean?
Both measures use profit in the numerator, but they divide by different amounts. Confusing markup with margin can make a selling price miss the intended profitability target.
Why a 30% target margin is not cost multiplied by 1.3
A target margin measures profit as a share of the selling price. Solving for that price requires division by one minus the margin, rather than applying the same percentage as a markup.
Does a 20% price discount reduce profit by only 20%?
When unit cost stays unchanged, a price reduction directly compresses the gap between price and cost. Profit can fall much faster than the selling price.
Currency converter ↗
Should you multiply or divide when converting currencies?
The direction of the quote determines the operation. Write the rate as an equation with currency units before converting an amount, rather than treating an unlabeled number as interchangeable in both directions.
How to calculate a cross exchange rate from a common base
If two currencies are quoted against the same base, their ratio can produce a cross rate. The quote timing and conventions must be compatible for that comparison to be meaningful.
A better exchange rate but less money received? Include the fees
Compare the exchange rate together with fixed charges, percentage charges and possible recipient-side deductions. One attractive headline number does not establish the best outcome.
Return on investment calculator ↗
ROI is more than the sale price: include income and expenses
Record sale proceeds, income received, original cost and additional expenses separately. Omitting or double-counting one category can change the return percentage substantially.
Why a multi-year ROI is not an annual return
Simple ROI measures the total return over the holding period. Investments with different durations cannot be compared fairly by treating that percentage as if each were earned in one year.
How to enter an investment loss without counting fees twice
A negative ROI is a valid result and should not be replaced with zero. Establish whether proceeds are gross or already net of charges, then use one consistent accounting convention.
Debt-to-income ratio calculator ↗
Why debt-to-income ratio uses gross income rather than take-home pay
A standard DTI calculation commonly divides monthly debt payments by gross monthly income. A household cash budget needs take-home income, so the two views should not be treated as interchangeable.
For DTI, should you enter debt balances or monthly payments?
Debt-to-income ratio measures monthly payment obligations, not the sum of every outstanding loan balance. The input needs to match the monthly cash-flow definition.
Reducing DTI: lower payments or higher income?
Both the numerator and denominator can change debt-to-income ratio. Paying down principal does not necessarily reduce the contractual monthly payment immediately, so an overpayment cannot simply be subtracted from monthly obligations.