Finance Calculations
Interest, loans, investments and taxes — learn how every financial number is derived before you plug it into a calculator.
42 calculations published in this category.
Retirement
How To Calculate 401(k) Growth
A 401(k) projection answers a specific question: at a fixed contribution and a fixed return, what will the account be worth at retirement, and how much of that did the employer match create? The arithmetic is a future-value calculation with two additions a year, yours and the match.
FV = B(1+r)^t + (C + M) x [((1+r)^t - 1) / r]
How To Calculate Annuity Payments
Given a balance, a return and a number of years, the payment that exactly exhausts the account is one algebraic step away. The hard part is not the formula — it is recognising that a level payment for a fixed period is a very specific promise that real markets do not make.
PMT = PV x r x (1 + r)^n / ((1 + r)^n - 1)
How To Calculate Roth IRA Growth
A Roth IRA is funded with money that has already been taxed, and qualifying withdrawals are tax free. The benefit is not a deduction today but decades of compounding that the tax authority never touches.
Future value = sum of contributions x (1+r)^t, plus existing balance grown
How To Calculate Your FIRE Number
The FIRE number is your annual spending divided by the withdrawal rate you consider sustainable. At 4% that means twenty-five times a year of expenses — a figure that is easy to compute and very easy to compute on the wrong expenses.
FIRE Number = Annual Spending / Safe Withdrawal Rate
Loans & Debt
How To Calculate A Car Lease Payment
A lease payment is the interest on the whole car plus the depreciation you consume while you drive it. Both halves are set by the price, the residual value and the money factor, so a small change in any of them moves the monthly figure.
Payment = depreciation + finance charge
How To Calculate EMI
An equated monthly instalment is the fixed payment that repays both principal and interest over a set term. It stays the same every month, but the split between interest and principal shifts steadily in the borrower's favour.
EMI = P x r x (1+r)^n / ((1+r)^n - 1)
How To Calculate Refinance Savings
Refinancing replaces one loan with another, usually at a lower rate. The monthly saving is the obvious gain, but closing costs and a possibly longer term mean the break-even point and the lifetime interest matter just as much.
Saving = old payment - new payment; Break-even = costs / monthly saving
How To Calculate Student Loan Payments
A student loan repaid on the standard plan uses the same annuity formula as any other instalment loan. The balance, the rate and the term set the payment, and the term is usually the most powerful lever on total interest.
Payment = P x r x (1+r)^n / ((1+r)^n - 1)
Home Buying
Personal Finance
How To Calculate A Pay Raise
A raise has three numbers that matter: the new salary, the extra pay per period, and whether the increase beats inflation. A nominal raise that falls below inflation is a cut in real terms, even though the paycheck is bigger.
New salary = old salary x (1 + raise%)
How To Calculate A Paycheck
Gross pay is what you earn; net pay is what reaches your bank account. The gap is income tax, payroll taxes and any retirement or benefit contributions, and it is often large enough to change how you budget.
Net pay = gross - income tax - payroll tax - contributions
How To Calculate Savings Account Interest
Savings account interest depends on the rate and how often it compounds. Monthly compounding earns a little more than annual compounding at the same headline rate, and regular deposits add to the balance faster than the interest alone.
Balance = principal x (1 + rate/n)^(n x t)
Loans
How To Calculate An Amortization Schedule
An amortization schedule is the month-by-month ledger of a fixed-rate loan: every payment is the same size, but the split between interest and principal shifts a little each month. Early on almost everything goes to interest; near the end almost everything goes to principal. The monthly payment comes from one formula, and from it you can read off the first month's interest, the principal that payment retires, and the balance left afterwards.
M = P x r / (1 - (1 + r)^-n)
How To Calculate APR
The APR is the interest rate that would produce your loan's cash flows if the fee were rolled into the rate. It answers a fairer question than the advertised nominal rate: what single annual rate, applied to the money you actually received, reproduces the payments you actually make?
Solve for i: P - F = sum of pmt / (1 + i)^k
How To Calculate Auto Loan Payment
A car loan is an amortizing loan like any other: a fixed payment retires the balance over the term. The car-specific wrinkle is the trade-off between payment size and total cost, and the effect of a trade-in and sales tax on the amount actually financed.
M = P x r / (1 - (1 + r)^-n)
Banking
Investing
How To Calculate Bond Yield
A bond's yield is the income it pays divided by what you paid for it. Because bonds trade at prices above or below their face value, two bonds with the same coupon can yield very different amounts, and the price move at maturity is part of the return.
Current yield = annual coupon / price paid
How To Calculate Investment Return
Total return measures how much an investment gained in percentage terms. Annualised return converts that into a per-year rate, which is the only fair way to compare a three-year holding with a ten-year one.
Total return = (final value - initial) / initial; Annualised = (1 + total)^(1/years) - 1
How To Calculate IRR
The internal rate of return is the discount rate that makes an investment's net present value exactly zero. It is the break-even rate the project must beat, and it lets you compare projects of different sizes on a single percentage scale.
NPV = 0 at the rate r, so r is the IRR
How To Calculate NPV
Net present value asks a single sharp question: after discounting every future cash flow back at the rate you require, does the investment create or destroy value? It is the most reliable single test in capital budgeting because it works in money rather than in ratios.
NPV = -C0 + sum of CF / (1 + r)^t
How To Calculate The Rule Of 72
The rule of 72 is a mental shortcut for doubling time: divide 72 by the annual return and you get roughly how many years it takes for money to double. It is fast, memorable and close enough for nearly every rate you will meet.
Doubling time = 72 / annual return percent
Business
Investment
How To Calculate CAGR
CAGR compresses a messy multi-year history into one smooth annual rate. Because it reports the same kind of number for a seven-year stock hold and a five-year revenue line, it is the standard way to put two very different histories on one scale.
CAGR = (Ending Value / Beginning Value)^(1/n) - 1
How To Calculate Compound Interest
Compound interest is interest that earns interest. Once interest is added to your balance, that added amount starts earning too — which is why long horizons grow faster than people expect.
A = P(1 + r/n)^(nt)
How To Calculate Future Value
Future value of an annuity projects what a stream of equal contributions becomes. Because every deposit compounds for a different length of time, this is the formula retirement plans actually depend on — not the lump-sum one.
FV = PMT x (((1 + r)^n - 1) / r)
How To Calculate Present Value
Present value runs the time value of money backwards: instead of growing today's money forward, it tells you what a future payoff is worth right now. Every bond price, lease valuation and capital budgeting decision rests on this one operation.
PV = FV / (1 + r)^n
How To Calculate Purchasing Power
Purchasing power translates an amount of money into what it can actually buy. Every long-term plan denominated in fixed dollars is quietly wrong until this adjustment is applied.
Real Value = Nominal Amount / (1 + i)^n
How To Calculate ROI
Return on investment expresses what you gained as a percentage of what it cost you. That single normalization is why ROI survives every criticism leveled at it: it works on a stock, a rental property, or a training program with exactly the same arithmetic.
ROI = (Current Value - Cost) / Cost x 100%
How To Calculate Simple Interest
Simple interest pays only on the original principal and never reinvests itself. That makes it the easiest interest calculation to verify by hand — and the right model for most short-term loans, bonds and treasury bills.
I = P x r x t
Saving
How To Calculate CD Return
A certificate of deposit pays a fixed rate for a fixed term in exchange for leaving your money untouched. The growth depends on whether interest compounds and on how early withdrawal penalties would bite, but the core number is simply the deposit grown at the APY.
A = P(1 + r)^t
How To Calculate Inflation Adjusted Value
Inflation quietly erodes the buying power of money. A sum held in cash loses value every year even though its number stays the same. This calculator converts between nominal amounts and real, inflation-adjusted amounts so you can compare figures honestly across time.
Real value = nominal / (1 + i)^t
How To Calculate How Long It Takes To Reach A Savings Goal
A savings goal has three moving parts — what you already have, what you add each month, and what compounding quietly adds on top. The third one is the reason rounding your monthly figure to a nice number can push your finish line out by years.
n = ln((FV x r + PMT) / (PV x r + PMT)) / ln(1 + r)
Credit & Debt
How To Calculate Credit Card Payoff Time
Paying a fixed amount every month retires a revolving balance on a predictable schedule — and that schedule can be written as a closed-form equation rather than simulated line by line. The catch is a boundary condition the formula cannot cross: pay only the interest and the balance never falls.
n = -ln(1 - (rm x B) / P) / ln(1 + rm)
How To Calculate Debt-To-Income Ratio
The debt-to-income ratio answers the question a lender is actually asking: not how much you owe, but whether the monthly payments fit inside your income. It takes two numbers and it decides mortgage approvals.
DTI = Total Monthly Debt Payments / Gross Monthly Income
Taxes
How To Calculate Effective Tax Rate
Your effective tax rate is what you actually paid, expressed as one number. It is always lower than your headline bracket on the same tax — and often badly misleading if you stop at federal income tax and ignore payroll.
Effective Tax Rate = Total Tax / Gross Income
How To Calculate GST
Goods and services tax is a single tax applied to most supplies of goods and services. Adding it multiplies the base price; removing it divides, and the same rate can be split between national and regional shares.
GST = base x rate
How To Calculate Tax Bracket
A progressive tax system taxes each slice of income at its own rate. Your bracket is the rate on the last dollar you earn, not the rate on all of it, and the difference between the two is the source of most confusion about taxes.
Tax = sum of (income in each bracket x that bracket's rate)
How To Calculate VAT
Value added tax is charged on the price of goods and services and is normally included in the price you see. Adding it is a multiplication; removing it is a division, and mixing the two up is the most common VAT error.
Gross = net x (1 + rate)