Finance Calculator

Because one equation has to describe both money coming to you and money leaving you, and the only way to tell those apart is a sign. The convention is that cash leaving you is negative and cash arriving is positive. Depositing $10,000 to let it grow is a present value of -10,000; borrowing $10,000 is +10,000. If every number you enter has the same sign there is no answer to find, which is why the calculator asks for at least one of each when solving a rate.

This one is general. The loan calculator, the investment calculator and the annuity calculators are each this same equation with some of the five variables fixed and friendlier labels on the rest. Use those when your question fits their shape, and use this when it does not — when you need to solve for the term, or mix a starting balance with a payment and a target ending balance.

Periods, not years. If you set periods per year to monthly, then a thirty-year term is 360 periods and the annual rate is divided by twelve to get the rate charged each month. Mixing these up is the most common way to get a wrong answer out of any financial calculator: 30 periods at 7% monthly is two and a half years, not thirty.

Rent, leases and many insurance premiums are paid in advance, at the start of the period. Almost every loan and most savings plans pay in arrears, at the end. The choice matters: each beginning-of-period payment earns one extra period of interest, so an annuity due is worth exactly (1 + periodic rate) times the equivalent ordinary annuity.

There are three different reasons, and the calculator tells you which one applies. Your cash flows may all point the same way, in which case nothing can balance them. The rate that would balance them may be above 200% a year, the most this calculator will report. Or, more rarely, two different rates may both balance them, which happens when the payment stream changes direction more than once; there is no single right answer to report, so it says so rather than picking one.

Nominal. The annual rate you enter is divided by the number of periods a year to get the periodic rate, and a solved rate is multiplied back the same way. That is the convention Regulation Z Appendix J uses for loans and the one Regulation DD uses when it defines an interest rate as not reflecting compounding. It is not an APY, and it is not an APR either, because no fees are involved.

Because the answer to "how long until I reach $100,000" almost never lands exactly on a payment date. A result of 103.4 monthly periods means you pass your target partway through the 104th month. Rounding it up to a whole period would quietly overstate what you end with, so the fractional answer is shown as it is.

A self-check. Once a variable is solved, all five values are substituted back into the governing equation, which must come to zero. The residual is how far from zero it actually came, and it should be a vanishingly small number. A residual that is not near zero would mean the solver had not converged, and seeing it is better than trusting it.