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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negative values for owed balances and money paid into the account, positive values for balances in your favor and money withdrawn from the account.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. |
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:
These equations are similar to those used to calculate Population Increase , but they allow you to specify interest increase and payments as separate variables.
- 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.
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).
Here is a table of equations for the forms this problem can take, including the variations created by selecting payment at beginning and payment at end:Math NotesWhen 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).
Payment at beginning Payment at end ir = Solved by iteration ir = Solved by iteration
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.
Status indicator: There is a status indicator at the bottom of the calculator display to alert you that the computation is not complete. This indicator is meant to remind you that new numbers have been entered but a value button has not yet been pressed, which means the displayed values may not represent a consistent result.
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.
While reviewing old access logs at www.arachnoid.com, I noticed some visitors had been trying to specify values for Financial Calculator to save time whern computing common problems. This is a useful feature, so I have added it to the current version of Financial Calculator.
Here is an example of an URL that specifies values for Financial Calculator:
http://www.arachnoid.com/lutusp/finance.html?pv=0&fv=100000&np=200&ir=1&pb=falseIf you click the link above, it will reload this page and insert the values listed at the right. This feature allows you to predefine a problem in a link to this page.
In this example problem, the defined values are pv, fv, np, and ir. Because four of the five financial variables have been defined, the fifth variable (pmt) will be calculated as the page loads.
Here is an example URL that a Web page designer might create to call this page with predefinend values:
<a href="http://www.arachnoid.com/lutusp/finance.html?pv=0&fv=100000&np=200&ir=1&pb=false">compute PMT</a>
The basic URL syntax for using this feature looks like this:
page_name.html?name1=value1&name2=value2&name3=value3 (etc.)
Normally the calling parameters are written into the links of a Web page that calls this page.
The idea of this feature is that if a caller provides any four of the five required financial variables, the fifth value will be computed. If fewer or greater than four values are provided, they are accepted into the calculator, but no computation is performed (and the status indicator alerts you that the computation is not complete).
There is one special variable supported by this feature that is not named in the formal description provided earlier (and that is not counted in the total of four financial values) — the value pb, which means "payment at beginning." If you set this value to "true" or "false" in a calling URL, the calculator will accept your choice and compute accordingly. Defining this value is optional, but if you want consistent results, it's a good idea to specify it.
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