Financial calculators

Work out what a loan really costs, how fast savings compound, and what you can afford — using the same formulas banks use.

What these calculators actually model

Nearly everything here reduces to one idea: money has a price over time, and that price compounds. A loan payment is the constant amount that drives a balance to zero over a fixed term; a savings projection is the same arithmetic run in reverse. Once you can see the schedule rather than just the monthly figure, most financial questions stop being mysterious.

That is why the amortization breakdown matters more than the headline payment. Early in a mortgage almost the whole payment is interest, because interest is charged on a balance that has barely moved. The crossover point — the month where principal finally exceeds interest — is the single most useful number for deciding whether an overpayment is worth making, and it is invisible unless something shows you the schedule.

Rates that look alike and are not

A nominal rate, an APR and an APY can all describe the same loan and all differ. The nominal rate ignores compounding entirely. The APY folds compounding in, so 12 percent compounded monthly is an APY of 12.68 percent. The APR is meant to fold in fees as well, which is what makes it the comparable number between lenders — and also what makes two APRs incomparable when the fee structures differ.

Compounding frequency is the quiet variable. The same stated rate produces a different balance depending on whether it is applied yearly, monthly or daily, and over a thirty year term that gap is not small. Where a calculation depends on frequency, it is stated rather than assumed.

Frequently asked questions

What is the difference between an interest rate and an APR?

The interest rate is the cost of borrowing the principal alone. The APR adds the fees required to obtain the loan — origination charges, points, some closing costs — and expresses the total as a single yearly percentage. So the APR is at or above the interest rate, and it is the number to compare between lenders. It still assumes you hold the loan to term, which is why a loan you expect to refinance early can be cheaper than its APR suggests.

Why is almost all of my early mortgage payment going to interest?

Because interest is charged on the outstanding balance, and at the start the balance is at its largest. The payment is fixed, so whatever is left after interest goes to principal — very little at first. As the balance falls the interest portion shrinks and the principal portion grows, slowly at first and then quickly. The month where the two cross over typically falls somewhere past the halfway point of the term, not at the middle.

Does compounding frequency really change the outcome?

Yes, and more than most people expect over long horizons. A nominal 12 percent compounded annually returns 12 percent in a year; compounded monthly it returns 12.68 percent; compounded daily, 12.75 percent. On a single year that gap looks trivial. Run it for thirty years and the daily-compounded balance ends materially ahead, because the difference itself compounds.

Do these calculators account for tax?

Only where the calculator says so. The income tax, capital gains, paycheck and sales tax pages model tax directly and name the assumptions they make. The rest — mortgage, savings, retirement projections — work in pre-tax terms unless stated, because tax treatment depends on jurisdiction and on circumstances no calculator can see. Treat a projection as arithmetic, not as a filing.