Calculator Methodology

Budget Folders uses standard financial formulas drawn from industry practice, academic finance, and IRS publications. This page documents the exact formulas, variables, and assumptions behind every calculator.

Overview

Every calculator on Budget Folders implements a well-established mathematical formula — the same ones taught in finance courses, used by banks, and published in financial planning literature. We do not use proprietary models, black-box algorithms, or undocumented heuristics.

Where calculators involve assumptions (such as average investment returns or inflation rates), we document those assumptions below and allow users to override them with their own estimates whenever possible.

1. Loan & Mortgage Amortization

Used in: Mortgage Calculator, Loan Calculator, Auto Loan, Student Loan, Personal Loan, Business Loan, and Mortgage Payoff Calculator.

Standard amortizing loans use the annuity payment formula to calculate the fixed monthly payment required to fully repay the principal over a given number of periods at a fixed periodic interest rate.

Monthly payment formula

M = P × [r(1 + r)^n] / [(1 + r)^n − 1]

MMonthly payment amount

PPrincipal loan amount

rMonthly interest rate (annual rate ÷ 12)

nTotal number of monthly payments (years × 12)

Example: A $320,000 mortgage at 7.0% annual interest over 30 years: r = 0.07 ÷ 12 = 0.005833; n = 360; M = 320,000 × [0.005833 × (1.005833)^360] ÷ [(1.005833)^360 − 1] ≈ $2,129/month.

The amortization schedule is then generated month-by-month: each period's interest portion = remaining balance × r; principal portion = M − interest; new balance = old balance − principal portion.

2. Compound Interest

Used in: Compound Interest Calculator, Savings Calculator, Investment Calculator, Retirement Calculator, 401(k) Calculator, IRA Calculator.

Future value (lump sum)

FV = PV × (1 + r/n)^(n×t)

FVFuture value

PVPresent value (initial investment)

rAnnual interest rate (decimal)

nCompounding periods per year

tTime in years

Future value with recurring contributions

FV = PV×(1+r/n)^(n×t) + PMT × [(1+r/n)^(n×t) − 1] / (r/n)

PMTRegular contribution per period

PVInitial lump-sum principal

rAnnual interest rate (decimal)

nCompounding periods per year

tTime in years

Compounding frequency options include annually (n=1), quarterly (n=4), monthly (n=12), and daily (n=365). Monthly compounding is the most common for savings accounts and investment accounts.

3. Retirement Projection

Used in: Retirement Calculator, 401(k) Calculator, IRA Calculator.

Retirement projections combine the compound interest formula for the accumulation phase with an annuity withdrawal formula for the distribution phase.

Retirement withdrawal sustainability

PMT = PV × r / [1 − (1 + r)^(−n)]

PMTSustainable monthly withdrawal

PVTotal retirement savings at retirement age

rMonthly portfolio return rate

nMonths of retirement (life expectancy − retirement age)

Default assumptions (all overridable):

Annual investment return during accumulation: 7% (historical US stock market average, inflation-adjusted ~5%)
Annual return during retirement: 4–5% (more conservative allocation)
Inflation rate: 3% annually
Life expectancy: 90 years (can be adjusted)
Social Security not included by default (can be added as additional income)

4. Tax Calculation Methodology

Used in: Income Tax Calculator, Salary & Paycheck Calculator.

Federal income tax is calculated using marginal (progressive) tax brackets as published by the IRS. The tax owed on each bracket is computed separately and summed.

2024 Federal Tax Brackets (Single filers)

Rate	Taxable Income	Tax owed on bracket
10%	$0 – $11,600	$0 + 10% of amount over $0
12%	$11,601 – $47,150	$1,160 + 12% of amount over $11,600
22%	$47,151 – $100,525	$5,426 + 22% of amount over $47,150
24%	$100,526 – $191,950	$17,168.50 + 24% of amount over $100,525
32%	$191,951 – $243,725	$39,110.50 + 32% of amount over $191,950
35%	$243,726 – $609,350	$55,678.50 + 35% of amount over $243,725
37%	Over $609,350	$183,647.25 + 37% of amount over $609,350

Tax calculators apply the standard deduction ($14,600 for single filers in 2024, $29,200 for married filing jointly) before applying brackets, unless itemized deductions are specified. FICA taxes (Social Security 6.2% up to $168,600 and Medicare 1.45%) are calculated separately and added to the total tax burden.

5. Inflation Adjustment (CPI)

Used in: Inflation Calculator, Retirement Calculator, Savings Calculator.

Future value adjusted for inflation

FV_real = FV_nominal / (1 + i)^t

FV_realFuture value in today's purchasing power

FV_nominalFuture value in nominal (face-value) dollars

iAnnual inflation rate (decimal)

tYears into the future

The US Bureau of Labor Statistics (BLS) Consumer Price Index (CPI) is used as the reference for historical inflation. The default assumed future inflation rate is 3%, consistent with the Federal Reserve's long-term target of approximately 2–3%. Historical CPI data is used when calculating the purchasing power of past dollar amounts.

6. ROI and CAGR Formulas

Used in: ROI Calculator, Investment Calculator.

Return on Investment (ROI)

ROI = (Net Profit / Cost of Investment) × 100

Net ProfitFinal value − Initial investment

Cost of InvestmentInitial investment amount

ROIPercentage return (not annualized)

Compound Annual Growth Rate (CAGR)

CAGR = (Ending Value / Beginning Value)^(1/t) − 1

Ending ValueValue at end of period

Beginning ValueValue at start of period

tNumber of years

CAGRAnnualized growth rate (decimal)

Global Assumptions

Investment return: 7% annually (pre-tax, nominal). This approximates the long-term historical average annual return of the US stock market (S&P 500). Past performance does not guarantee future results.
Inflation: 3% annually. Consistent with the Federal Reserve's target range and long-run historical averages.
Mortgage PMI: Applied when loan-to-value ratio exceeds 80%. PMI rate default is 0.5% annually of the loan balance.
Tax year: 2024 federal tax brackets and standard deductions are used as defaults. State taxes are not included in federal-only calculations.
Compounding: Monthly compounding is used as the default for most savings and investment calculators.
Loan payments: All loan calculators assume equal monthly payments (fully amortizing), unless otherwise specified.

Limitations and Disclaimer

All calculators provide estimates based on the inputs and assumptions described above. Real-world results will differ due to:

Variable interest rates (particularly for adjustable-rate mortgages)
Changes in tax law after the date of last review
Actual investment returns varying from historical averages
Fees, penalties, and other costs not captured in simple formulas
Individual financial circumstances and lender-specific terms

Results are for educational and planning purposes only and do not constitute financial, tax, legal, or investment advice. Consult a qualified financial professional before making financial decisions. Full disclaimer

Last updated: January 15, 2025. Tax brackets reflect 2024 IRS Publication 505 data.