Methodology

This page explains how ManyTools calculators compute their results. We publish it because a calculator is only as trustworthy as the math behind it, and you deserve to see that math and the sources we relied on. Each calculator is built on a standard, well-documented formula rather than an opaque script, the formula is checked against worked examples before the tool is published, and we list the authoritative references that define the underlying concepts.

The page is organized by computational engine. A single engine powers a family of related tools, so the explanation below covers every tool that shares it. As we add new engines, we add a new section here.

Amortization engine (loans & mortgages)

The amortization engine powers our mortgage, home loan, FHA, home equity, personal, student, and auto-refinance calculators, along with the general loan, loan payment, loan interest, APR, amortization, and loan payoff tools. An amortizing loan is repaid in equal periodic payments, where each payment covers the interest due on the current balance and then reduces the principal.

The monthly payment formula

We compute the fixed monthly payment with the standard amortization formula:

• M is the monthly payment (principal and interest).
• P is the principal, the amount financed. For a purchase, that is the price minus the down payment.
• r is the monthly interest rate, equal to the annual rate divided by 12.
• n is the total number of monthly payments, equal to the term in years times 12.

When the interest rate is zero, the formula above is undefined, so the engine falls back to dividing the principal evenly across the term (P divided by n). Each tool then builds a full amortization schedule by applying interest to the running balance each month, subtracting the principal portion, and repeating until the balance reaches zero. Total interest is the sum of every payment minus the amount borrowed.

Taxes, insurance, and extra payments

For mortgage-type tools, property tax and homeowners insurance are entered as annual amounts, divided by 12, and added to the monthly principal-and-interest figure, with monthly HOA dues added on top. This reflects the common “PITI” structure (principal, interest, taxes, and insurance) that lenders use. The payoff tool applies any extra monthly payment directly to principal, which lowers the balance that future interest is charged against and shortens the schedule.

Sources

• Consumer Financial Protection Bureau, Owning a Home and consumerfinance.gov for definitions of amortization, principal and interest, APR, and mortgage payment components.
• The amortization payment formula is a standard result of financial mathematics (the present value of an annuity) and is not specific to any one lender or product.
• For tax-related figures, the IRS is authoritative: Topic No. 456, Student Loan Interest Deduction and Publication 936, Home Mortgage Interest Deduction.

Limitations

These tools assume a fixed interest rate and equal monthly payments. They do not model variable rates, mortgage insurance premiums, origination fees, biweekly schedules, or lender-specific rounding unless a tool states otherwise. Your actual figures may differ from a lender or servicer. Treat every result as an estimate, as described in our Terms.

Engines we are adding next

ManyTools is expanding beyond loan math. As each new engine ships, we will document it here in its own section with the same structure: a plain-language explanation, the exact formula, sources, and limitations. Planned engines include percentage and ratio math, date and time calculations, and grade and GPA scoring. This section is a placeholder until those tools are live, so the page grows alongside the library rather than being backfilled later.

How we review and update

Before a calculator is published, its output is checked against worked examples and, where a public authority defines the concept, against that source. Each tool page shows a “Last updated” date. If you spot a discrepancy, email hello@getorionscomet.com and we will review it.