How Extra Payments Pay Off a Loan Early
See how extra monthly payments and lump sums change a loan's payoff date, why timing matters, and what to verify with your lender first.
Companion tool: Loan Payoff Calculator
Guides
The ideas behind the calculators — written by the person who builds them, with every number verified the same way the tools are.
Tallyloom's tools deliberately show their formulas, but a formula on a results page can only say so much. These guides are where the reasoning goes: why the mathematically optimal debt strategy is not always the one people finish, how extra payments shorten a loan, what heart-rate zones estimate, how major citation styles differ, and how to calculate a tip. The collection also covers compound interest, password entropy, invoices, and the limits of BMI.
Every number in these articles is worked through in full and computed with the same code that powers the companion tool, so the article and the calculator can never quietly disagree. Each guide names its sources, links the tool it pairs with, and carries a review date. Read one before you use its calculator and the output stops being a number you have to trust and becomes one you can check.
Heart-Rate Zones by Age: A Practical Guide
Age-based training zones, the 220-minus-age estimate, the Karvonen method, and when medication or health history makes a generic chart unreliable.
Companion tool: Heart Rate Zones Calculator
Works Cited Examples: APA 7, MLA 9, and Chicago 18
Compare website, book, and journal references across three major styles, including missing authors, missing dates, DOIs, and in-text citations.
Companion tool: Citation Generator
How to Calculate a Tip and Split the Bill
Quick mental math for common tip percentages, pre-tax versus after-tax examples, bill splitting, and when a service charge is not a voluntary tip.
Companion tool: Tip Calculator
Debt Snowball vs. Avalanche: The Math and the Psychology
The avalanche method always wins on paper — so why do so many people pay off more debt with the snowball? A worked example with real numbers, and how to choose.
Companion tool: Debt Snowball Calculator
What Goes on an Invoice (and How to Follow Up When It Isn't Paid)
The elements every professional invoice needs, the payment terms that actually get you paid, and a calm escalation path for overdue invoices.
Companion tool: Invoice Generator
Password Entropy, Explained: Why Length Beats Complexity
What entropy bits actually measure, how long different passwords survive a modern cracking rig, and why four random words beat P@ssw0rd! every time.
Companion tool: Password Generator
How Compound Interest Actually Works
The formula behind compound growth, what compounding frequency really changes, the Rule of 72 — and a worked 10-year example you can verify yourself.
Companion tool: Compound Interest Calculator
What BMI Does — and Doesn't — Tell You
Where the BMI formula came from, what the standard categories mean, and the well-documented cases where the number misleads.
Companion tool: BMI Calculator