A mortgage is a loan secured by property — the lender funds the purchase, and you repay over time with interest. Most mortgages are amortizing loans: each payment covers interest first, with the remainder reducing the principal. In the US, the conventional 30-year fixed-rate mortgage represents 70–90% of all mortgages.
M = monthly P&I payment | P = principal (loan amount)
r = monthly rate (annual rate ÷ 12) | n = total number of payments
Lenders typically require your total PITI payment to be ≤ 28% of gross monthly income (front-end ratio) and total debt ≤ 36–43% (back-end ratio).
- PMI: Required when down payment is below 20%. Costs 0.3–1.9% of the loan annually. Drops off once LTV reaches 80%.
- Biweekly payments: Paying half the monthly payment every 2 weeks results in 13 full payments per year instead of 12 — saving significant interest and cutting years off the loan.
- Extra payments: Applied directly to principal, they reduce the balance faster and shrink total interest paid. Even $100/mo extra on a 30-year loan can save tens of thousands.
- HOA fees: Common for condos and planned communities. Annual HOA fees typically run under 1% of property value.
- Refinancing: Can lower your rate or shorten the term, but involves closing costs. Calculate break-even (months to recover costs via lower payments) before refinancing.
- Extra monthly payments: Even small amounts reduce principal faster and cut total interest paid significantly over time.
- Biweekly plan: 26 half-payments = 13 full payments per year, equivalent to 1 extra month per year.
- Lump-sum payments: One-time windfalls (bonuses, tax refunds) applied to principal can shave years off the schedule.
- Refinancing to shorter term: Moving from 30 to 15 years typically halves total interest paid, at the cost of higher monthly payments.
A personal loan is an unsecured installment loan — you borrow a fixed amount, then repay it in equal monthly payments over a set term. Unlike mortgages or auto loans, no collateral is required, so interest rates are typically higher (6–36% APR depending on credit score).
Interest Rate is the cost of borrowing the principal. APR (Annual Percentage Rate) includes the interest rate plus fees (like origination fees), making it the true cost of the loan. Always compare APRs — not just rates — when shopping for loans.
- A credit score above 720 typically qualifies for the best rates. Check and improve your score before applying.
- Shorter loan terms cost less in total interest, even though monthly payments are higher.
- Making extra principal payments reduces the balance faster and cuts total interest paid.
- Watch for prepayment penalties — some lenders charge a fee if you pay off early.
An auto loan is a secured installment loan where the vehicle serves as collateral. Lenders typically offer terms from 24 to 84 months. The longer the term, the lower the monthly payment — but the more you pay in total interest, and the higher the risk of being "underwater" (owing more than the car is worth).
Total Cost = (Monthly Payment × Term) + Down Payment + Trade-in Value
- Depreciation: New cars lose 15–20% of value in year 1. Buying a 1–2 year old used car can save thousands.
- Down payment: Aim for 20% on new, 10% on used to avoid going underwater.
- Loan term: Avoid 72–84 month terms. Low payments feel good but cost significantly more in interest.
- Gap insurance: If your loan exceeds the car's value, gap insurance covers the difference if it's totaled.
- Pre-approval: Get pre-approved by your bank or credit union before visiting a dealership for negotiating leverage.
Amortization is the process of spreading loan payments across a fixed period. Each payment covers the interest accrued since the last payment, with the remainder reducing the principal. Early payments are mostly interest; later payments are mostly principal — this is called a "front-loaded" interest structure.
Principal portion = Monthly Payment − Interest portion
New Balance = Old Balance − Principal portion
- Even one extra principal payment per year on a 30-year mortgage can shave 4–5 years off the loan.
- Extra payments go entirely to principal, dramatically reducing future interest.
- Bi-weekly payments (half your monthly payment every 2 weeks) result in 13 full payments per year instead of 12.
This calculator solves for the required monthly payment given a loan balance, interest rate, and target payoff date. It uses the standard loan payment formula in reverse — starting from your desired outcome and computing what you need to contribute each month.
r = monthly interest rate | n = number of months
- Avalanche method: Pay minimums on all debts, then put extra money toward the highest-interest debt. Saves the most in interest.
- Snowball method: Pay off the smallest balance first for psychological wins. Research shows it improves follow-through for many people.
- Debt consolidation: Combining multiple high-rate debts into one lower-rate loan simplifies payments and may reduce total cost.
This calculator reverse-engineers the interest rate embedded in a loan offer. Given a loan amount, monthly payment, and term, it uses numerical iteration to find the exact rate — useful when a lender quotes a payment without clearly stating the APR.
Annual Rate = r × 12
- Dealers and lenders sometimes advertise monthly payments without prominently disclosing the rate — this tool reveals the true cost.
- Always compare annualized APRs across lenders, not just monthly payments, which can be manipulated by extending the term.
- A 1% difference in rate on a $200,000 loan over 30 years adds roughly $40,000 in total interest.
Compound interest is interest earned on both the original principal AND previously accumulated interest. This creates exponential growth — the longer the time horizon, the more powerful the effect. Einstein reportedly called it the "eighth wonder of the world."
A = final amount | P = principal | r = annual rate
n = compounds per year | t = years
APY = (1 + r/n)ⁿ − 1
To estimate how long it takes money to double, divide 72 by the annual interest rate. At 7%, money doubles in roughly 72 ÷ 7 ≈ 10.3 years. At 10%, it doubles in ~7.2 years.
- Daily compounding earns slightly more than monthly, which earns more than annually — but the difference is often small at typical savings rates.
- High-yield savings accounts and money market funds typically compound daily.
- The APY (Annual Percentage Yield) accounts for compounding frequency and is the true annualized return.
Simple interest is calculated only on the original principal — not on accumulated interest. It grows linearly over time and is common in short-term loans and some bonds.
Final Balance = P × (1 + r × t)
Compound interest is calculated on both principal and previously earned interest. It grows exponentially, and the gap between simple and compound widens significantly over long periods.
- Simple interest is used for short-term loans, car loans, and some bonds.
- Compound interest applies to savings accounts, mortgages, credit cards, and most investments.
- Credit cards compound daily — which is why carrying a balance is so costly over time.
This calculator projects the future value of an investment with a lump-sum starting amount plus regular monthly contributions, assuming a fixed annual return compounded monthly.
P = initial investment | C = monthly contribution
r = monthly return | n = months
- The S&P 500 has historically returned ~10% annually before inflation, ~7% after. Use 6–8% for long-term projections.
- Bond-heavy portfolios typically yield 3–5%. A 60/40 stock-bond portfolio averages ~7%.
- These are long-run averages — actual returns vary significantly year to year.
- 401(k) / 403(b): Pre-tax contributions, tax-deferred growth. 2024 limit: $23,000 ($30,500 if 50+).
- Roth IRA: After-tax contributions, tax-free growth. 2024 limit: $7,000 ($8,000 if 50+).
- Taxable brokerage: No contribution limits, subject to capital gains tax.
The most common rule of thumb is the 4% Rule: multiply your desired annual retirement income by 25 to get the nest egg you need. For example, to spend $60,000/year, you'd need $1,500,000. This assumes a balanced portfolio and a ~30-year retirement horizon.
Monthly Income = Nest Egg × 0.04 / 12
- By 30: Aim to have 1× your annual salary saved.
- By 40: 3× your annual salary.
- By 50: 6× your annual salary.
- By 60: 8× your annual salary (Fidelity benchmarks).
- Social Security: Claiming at 62 gives ~70–75% of full benefit; waiting until 70 gives ~124–132%.
A 3% annual inflation rate cuts purchasing power in half over 24 years. Retirement portfolios must generate returns that outpace inflation — which is why many advisors recommend keeping some equity exposure even in retirement.
The US uses a progressive tax system — you only pay the bracket rate on income within that bracket, not on all income. If you're in the 22% bracket, only the dollars above the 12% threshold are taxed at 22%.
- Marginal rate: The tax rate on your last dollar of income — the highest bracket you reach.
- Effective rate: Total taxes paid ÷ total income. Always lower than your marginal rate.
- Someone in the 24% bracket does not pay 24% on all income — only on the top slice.
Head of Household: $21,900
Only itemize if your deductions (mortgage interest, charitable gifts, state taxes) exceed the standard deduction.
Monthly = Annual ÷ 12
Bi-weekly = Annual ÷ 26
Weekly = Annual ÷ 52
Daily = Annual ÷ (Weeks × 5)
Hourly = Annual ÷ (Hours/Week × Weeks/Year)
- Base salary is just one component. Total compensation includes bonuses, equity (RSUs/options), health insurance, 401(k) match, PTO, and other perks.
- A 401(k) match of 4% on a $80,000 salary adds $3,200/year in value — essentially free money.
- When comparing job offers, always calculate total compensation, not just base pay.
- Research market rates on Glassdoor, Levels.fyi, LinkedIn Salary, and the Bureau of Labor Statistics.
- Always negotiate — studies show over 70% of employers expect it and have budget room.
- Consider negotiating signing bonuses, remote work flexibility, and equity in addition to base salary.
Inflation is the rate at which the general level of prices for goods and services rises over time, eroding purchasing power. If inflation is 3% annually, something that costs $100 today will cost $103 next year. Over 20 years at 3%, it costs $181.
Real Value = Nominal Value ÷ (1 + inflation rate)^years
- The Federal Reserve targets 2% annual inflation as a healthy benchmark for the US economy.
- The US experienced elevated inflation of 7–9% in 2022 due to supply chain disruptions and fiscal stimulus.
- Historically, the long-run average US inflation rate is approximately 3% per year since 1913.
- The CPI (Consumer Price Index) is the most commonly cited inflation measure, tracking a basket of typical consumer goods.
- TIPS: Treasury Inflation-Protected Securities adjust principal with CPI, protecting bond investors.
- Equities: Stocks have historically outpaced inflation over long periods.
- Real estate: Property values and rents tend to rise with or above inflation.
- I-Bonds: US Savings Bonds with rates tied directly to CPI — great for short-term inflation protection.
Time Value of Money (TVM) is the foundational concept that a dollar today is worth more than a dollar in the future — because today's dollar can be invested to earn returns. TVM underpins virtually every financial calculation: loans, investments, annuities, and valuations.
FV = Future Value (what it will be worth later)
r = Interest/discount rate per period
n = Number of periods
PMT = Periodic payment amount
FV = PV × (1 + r)ⁿ + PMT × [(1+r)ⁿ − 1] / r
- Bond pricing: A bond's price is the PV of its future coupon payments and face value, discounted at the market rate.
- Business valuation: DCF (Discounted Cash Flow) models use TVM to value companies based on projected future cash flows.
- Retirement planning: How much you need to save today (PV) to reach a future goal (FV).
- Loan structuring: Given a rate and term, what PMT makes PV = loan amount and FV = $0.
Sales tax is a consumption tax levied on the sale of goods and services. In the US, there is no federal sales tax — rates are set by individual states, counties, and cities, and can be layered. The combined rate varies widely: from 0% in Oregon, Delaware, Montana, New Hampshire, and Alaska to over 11% in some California and Louisiana jurisdictions.
Backing out tax: Pre-tax = Total ÷ (1 + rate)
Tax amount = Total − Pre-tax
Backing out is useful when a price tag already includes tax (common in some countries) and you need to know the pre-tax amount, or when calculating a merchant's tax liability from gross receipts.
- No sales tax: Oregon, Delaware, Montana, New Hampshire, Alaska.
- Lowest rates: Hawaii (4%), Wisconsin (5%), Maine (5.5%).
- Highest combined rates: Louisiana (~9.5%), Tennessee (~9.5%), Arkansas (~9.5%).
- Many states exempt groceries, prescription drugs, and clothing from sales tax.
