Peter Alfeld, --- Department of Mathematics, --- College of Science --- University of Utah
The applet on this page let's you bring up a financial calculatorthatyou can use to compute your loan payments, examine the evolution of yoursavings, or plan your retirement.
The calculator let's you explore the connections between 5financial parameters:
- n: the number of payments. These are usually monthly, butcould be any other time interval.
- The interest (p) in percent, paid perpayment. Thus if you make monthly payments at an annual interest rate of 12%p will equal 1%.
- The Principal Value, (PV). The amount ofmoney you borrow. Thus if PV is positive you take out a loan,if PV is negative, you put money into your account to startthings off.
- Your regular payment, (pmt). Financialcalculators usually require that a payment you make is negative, butto me a negative "payment" should mean you get money. Thus pmtis positive when you pay off a loan, and it's negative when you drawmoney out of an account.
- The Future Value, (FV), of your investment. It is zero if yousimply pay off a loan, positive if you save a certain amount of money,and negative if you are planning to pay off or refinance a balloonpayment at the end of your payment.
The menu below let's you look at several detailed examples showing thecalculator, a plot of the payment plan, and a detailed table of payments.
The image nearby shows what you should see on your screen afterclicking on the applet.
You need to specify the contents of four of the blue textfieldsand then click on the button labeled compute next to thefifth. The Calculator will compute the value of the fifth parameterand display it in the corresponding text window. You can also printor plot a payment plan.
Following is an explanation of the individual items on theCalculator:
- Textfields The central ingredients of the Calculator arethe blue textfields. They let you enter Data and they display data. To enter or modify data highlight the region ion the textfield youwant to change and type in the replacement. To make the program takenote of your change it is essential that you press the Enter or Return key.
- Compute Buttons For all financial parameters these causethe calculator to compute the parameter in the same row so as to beconsistent with the other four parameters.
- Increment Buttons These green Buttons let you useshortcuts to change the entries of the textfields. Their preciseeffects are explained below. You don't need to type Enter in thetextfield after using one of the increment buttons.
- Red Buttons These have specialized effects explained below.
- Row 1. The run # is incremented by 1 every time theCalculator is used.
- Row 2.
- Quit Clicking on this button causes the Calculator todisappear. If you called it from the applet on this page you can makeit reappear by clicking on the applet. If you are using it in standalone mode you need to restart it.
- Plot This causes a very rudimentary plot to be drawn thatis explained in Example 1.
- Print This causes a listing of the payment plan. You cansee it ion the Java Console or in the window from which you startedthe Calculator. Depending on your particular computing set up thislisting can be captured and put into a file.
- Update This button causes the contents of all textfieldsto be set equal to the internal values kept by the calculator at thattime. Actually the textfields should be up-to date all the time andso should need that button. But it's there so you can reassureyourself if you have any doubts.
- Status Label Next to the buttons in this row there is alabel telling you the current status of the calculator:
- ready This means you can compute any of the five parametersto make it consistent with the remaining four.
- consistent This means one of the parameters has beencomputed, and the five values you see are consistent.
- did not parse The calculator did not understand what numberyou just tried to tell it in one of the textfields.
- Floating Overflow The calculator tried to compute a numberthat is too large to be expressed in its internal number system.(That means its absolute value exceeds 10308.
- log of negative The calculator tried to compute thelogarithm of a negative number.
- no convergence The calculator failed to compute an interest rate.
- Row 3, n, the number of payments.Small increments change that number by 1, large increments by 12.(Think of 12 monthly payments being one yearly payment.) The Buttonlabeled x12 lets you enter the duration of the loan as a number ofyears followed by converting that number to the number of months.
- Row 4, interest. This is the interest rate in percent per payment.Small increments change the interest rate by 0.1, large ones by 1.The button labeled /12 lets you enter an annual interest rate andconvert it to the monthly interest rate.
- Row 5, Principal Value. A positive value indicates you havemoney to spend, a negative value means someone made an initial payment into your account. Small increments change the value by $1, large onesby $1000. The Round Button rounds the Principal Value to the nexthigher multiple of $1,000.
- Row 6, Payment. A positive value indicates you pay money, anegative one you receive money. Small increments change the paymentby $1.0, large ones by $10. The Round button rounds the payment tonext highest dollar.
- Row 7, Future Value. A positive value indicates you havemoney available after making payments, a negative value means youstill own money. Small increments change the value by $1, large onesby $1000. The Zero Button sets the Future Value to zero.
Since this is a mathematic page I'll have to tell you what's happeninginside the Calculator.
(1)
Then it is a simple exercise to verify that the key equationlinking our five parameters is
(2)
This equation can be solved explicitly for four of the fiveparameters:
(3)
To solve (2) for p a simple numerical technique(bisection) is used.
You can download this code and run it without a browser.You need two files
Download the files and invoke Loan.class like you would any Java code. For example, on a Unix system you type java Loan
Last change: [13-Mar-1999]
Copyright © 1998 Department of Mathematics, University of Utah
