Finance Calculator
Name
Value
Compute
Present Value
Future Value
Number of Payments
Payment Amount
Interest Rate per period, %
Payment At: Beginning End

Instructions: Type in known values, then press one of the buttons at the right for the desired unknown.

(to solve an example problem, press the "FV" button above)

Remember to use negative values for owed balances and money paid into the account, positive values for balances in your favor and money withdrawn from the account. Also enter the interest rate per period, not per year. If you are making monthly payments and have an annual interest rate, divide the annual rate by 12 (and see this math note). Thus, one period of an 8% annual rate is 8/12 and is entered as .666666.

Interest computation is not a simple matter of applying an equation, and many problems have more than one solution, only one of which is likely to be meaningful. If you get an interest rate that doesn't seem right, try entering an approximation of the expected rate, then press "IR" again.
The Tutorial
These equations solve problems that involve compound interest. With one exception, each kind of problem can be solved immediately, using a well-defined equation. The exception, as Isaac Newton discovered, is that interest computation requires iteration and may result in several solutions.

The variables used are:
  • pv (present value) = The starting balance in an account. This number can be zero, positive (when you take out a loan), or negative (when you make a deposit).
  • fv (future value) = The ending balance after a certain number of payment periods ( np ).
  • np (number of periods) = The number of payment periods, usually expressed in months.
  • pmt (payment) = The amount of each periodic payment, usually a negative amount.
  • ir (interest rate) = The interest rate on the account per period.

These equations are similar to those used to calculate Population Increase , but they allow you to specify interest increase and payments as separate variables.

An Example

Let's say you want to know how much money you will have in an investment that has an annual interest rate of 12%. The account has a starting balance of $0.00 and you are planning to deposit $100 per month. For the interest rate per period (per month in this case), divide the annual interest rate of 12% by 12 = 1% per month (is this correct?) . Result: in 10 years (120 months) you will have a balance of $23,003.87 (you may test this result with the calculator above).

When using these equations, be sure to use negative values for owed balances and money paid to the account, positive values for balances in your favor and money withdrawn from the account. For these formulas, enter percentages as ratios, thus 8% = 0.08 (yes, I know the financial calculator at the top of the page accepts percentages as integers, but these formulas are real math — no hand-holding).

These equations, with small variations, are used by most of the available financial calculators and spreadsheets that support financial functions.

There are several boundary conditions implicit in these equations (conditions for which no meaningful result can be obtained). Example: if a payment is chosen that exactly offsets the accrued interest per period and you try to solve for NP, that equation will break, because there are an infinite number of periods in that case.

Math Notes

Interest rate per period: This business of dividing an interest rate by 12 is not mathematically correct, but since the banks use this procedure it is wise to do it also, otherwise your numbers will not agree with those of the bank.

Interest (IR) computation: The case of IR cannot be solved without iteration (a method for which we are indebted to Isaac Newton). This calculator solves for IR using an efficient iteration method that will work for most problems, but a multiple-root possibility exists (more than one correct, if meaningless, result). If a particular problem will not yield an interest rate or produces a meaningless rate, you may want to try typing an estimate of the correct rate in the interest rate display window and pressing "Calc IR" again.