15-Year vs 30-Year Mortgage: Payment, Interest and Trade-offs
A shorter mortgage costs far less in interest but asks for a much higher monthly payment. A side-by-side example shows the size of both effects.
Money & Finance
Interest, loans, savings, pay and everyday money maths, explained with worked examples.
APR vs APY: What the Two Rates Really Tell You
APR and APY are two ways to quote the same rate. One ignores compounding and one includes it, and mixing them up can make a worse deal look better.
APR vs Interest Rate: What the Difference Means for a Loan
A loan with the lower interest rate is not always the cheaper loan. The APR folds in certain fees so offers can be compared, and a worked example shows how.
How to Calculate a Pay Raise and What It Is Worth After Inflation
A 3.5% raise on $52,000 is $1,820, but what does it buy? Learn the raise formulas, the effect of back-to-back raises, and how inflation changes the picture.
Compare Unit Prices: Which Size or Brand Is Really Cheaper?
The bigger pack is not always the better value. Divide price by quantity, use the same unit for both, and the cheaper choice becomes obvious.
The Compound Interest Formula, Step by Step
Compound interest is interest that earns interest. Here is the formula, a full worked example, and how to rearrange it to find the interest, the time or the rate.
Does Compounding Frequency Matter? Daily vs Monthly vs Yearly
Moving from yearly to monthly compounding adds a visible amount; moving from daily to continuous adds under a dollar. The numbers show where the gains run out.
Cost-Plus Pricing Step by Step: From Unit Cost to Shelf Price
Cost-plus pricing starts with what a product costs you and works up to a price. Follow the steps, including how fees and sales volume change the result.
Cost Ratios: COGS, Labor and Overhead as a Percent of Sales
A cost ratio divides one expense by your sales. It makes months of different sizes comparable and shows which costs are quietly growing.
Credit Utilization Ratio Explained: How to Calculate It
Credit utilization is a simple ratio of what you owe to what you could borrow. Here is how to work it out, why per-card figures matter, and how to lower it.
Debt Snowball vs Debt Avalanche: Which Payoff Method Wins?
Both methods pay debts off one at a time. One saves the most interest, the other clears the first debt sooner. A worked example shows the real size of the gap.
Debt-to-Income Ratio: How to Calculate It and What Counts
Lenders compare what you owe each month with what you earn. Here is the formula, which payments count, and how a new loan would change your ratio.
Dollars Off or Percent Off? Comparing Coupons, BOGO and 3-for-2
Different deals are quoted in different units. Convert each to a percentage of what you would pay and the best offer becomes easy to spot.
How Many Extra Sales Does a Discount Need to Pay for Itself?
Discounts cut the profit on every unit, so you have to sell more just to stand still. Here is the formula and a table showing how fast the required volume grows.
Gross, Operating and Net Profit: What Each One Tells You
A business can have three different profit figures from the same sales. This guide walks down the income statement and shows which question each one answers.
Gross Pay vs Take-Home Pay: Where the Difference Goes
Your paycheck is smaller than your salary divided by pay periods. Here is what comes out, why pre-tax deductions cost less than they appear, and how to estimate.
Hourly or Salaried? How to Compare Two Job Offers Fairly
A $24 hourly wage and a $52,000 salary are not comparable until you count hours and paid leave. Here is a simple method to line them up.
How Credit Card Interest Works: Daily Rates and Minimums
Card interest is charged on a daily balance, not a flat monthly fee. A worked example shows how the daily rate works and how long minimum payments really take.
How Loan Amortization Works: Where Each Payment Goes
Every payment on a fixed loan is the same size, but the split between interest and principal keeps changing. Here is how that schedule is built and read.
How Much to Save Each Month to Reach a Savings Goal
Pick a target, a deadline and an expected interest rate, and a short formula gives the monthly deposit. A 20,000 goal in five years is the worked example.
How Overtime Pay Is Calculated: Time-and-a-Half Worked Through
Overtime math is simple once you know the regular rate and the threshold. Follow worked examples for hourly, bonus and salaried pay.
How Sales Commission Works: Flat, Tiered and Marginal Rates
The same sales can pay very different commission depending on how the tiers are applied. This guide compares the three common structures with numbers.
How to Calculate a Break-Even Point in Units and Revenue
Your break-even point is the sales level where income equals costs. Here is the hand calculation in units and in revenue, plus how a price change moves it.
How to Calculate a Monthly Loan Payment by Hand
A loan payment comes from one short formula. Work through it with real numbers, see how term and rate change the total cost, and learn to check a lender's quote.
How to Calculate CAGR by Hand, Step by Step
CAGR turns a start value, an end value and a time span into one smoothed yearly rate. Here is the formula, a full calculation and the traps to avoid.
How to Set an Hourly Rate From Your Annual Income Goal
Freelancers and contractors who divide a salary by a full-time year end up with a rate that is too low. Start from billable hours instead and the maths changes.
How VAT Works: Adding and Removing It, and Sales Tax Compared
To remove 20% VAT you divide by 1.2, not subtract 20%. Follow the formulas, a supply-chain example, and a comparison with sales tax.
Inflation and Purchasing Power: What Your Money Buys Over Time
A rise in prices means each unit of money buys less. Here is how to measure inflation, project future prices and work out the value of cash that sits still.
Weekly, Biweekly or Semimonthly? Splitting Annual Pay by Period
Biweekly means 26 paychecks and semimonthly means 24. Here is how to divide a salary by period, budget by month, and spot the extra-paycheck months.
How Extra Payments Pay Off a Loan Faster, With Examples
Extra money sent to a loan goes straight at the balance, so the saving compounds. These worked examples show how much time and interest it can remove.
Pro Rata Pay: How to Prorate a Part-Time or Partial-Year Salary
A 24-hour week on a $52,000 full-time salary is $31,200 pro rata. See the full-time-equivalent method, how leave scales, and three ways to prorate a start date.
Real vs Nominal Interest Rates: Adjusting for Inflation
A 4% rate with 3% inflation does not grow your buying power by 4%. The real rate shows what is left once rising prices are taken out.
ROI Explained: The Formula, a Worked Example and Its Limits
ROI is simple to compute and easy to misuse. This guide covers the formula, an example that compares two projects, and the traps that make ROI misleading.
The Rule of 72: How Fast Does Money Double?
Divide 72 by the yearly percentage rate and you have a quick estimate of how many years it takes to double. Here is why it works and when it breaks down.
A Simple Sales Forecast: Projecting Revenue From Past Growth
You do not need special software to project next quarter's sales. Three simple methods, one data set and an honest look at what each assumes.
Simple vs Compound Interest: How the Gap Grows
Simple interest grows in a straight line and compound interest curves upward. A side-by-side example shows how small the gap is at first and how large it becomes.
Why 20% Off and Then 10% Off Does Not Equal 30% Off
Take 20% off, then another 10% off, and you save 28%, not 30%. Learn why stacked discounts combine this way and when the order of coupons matters.
Start Saving Early or Save More Later? What the Math Says
Ten early years of saving can match or beat thirty later ones, depending on the return. A side-by-side example shows exactly where the crossover happens.
What Is Included in a Mortgage Payment? PITI Explained
The loan repayment is only part of what you pay each month. Learn what PITI stands for, how escrow works, and how a down payment changes the monthly figure.
Why a 30% Markup Is Not a 30% Margin (and How to Convert)
Adding 30% to your cost does not leave you with a 30% margin. Learn why the two figures differ and how to convert between them without mistakes.