The free app, EZ Financial Calculators by Bishinew Incorporated, appears to have the features you want. This app lets you perform a variety of different financial calculations, with the option of emailing the results, and also accessing additional tables generated from your inputs, such as a table of interest and balance listed by number of months for the period of your compound interest calculation. This free app is ad supported, but the ads are unobtrusive, and only appear at the bottom of the screen. There is a paid version of the app that will also do stock and bond calculations, but the free app should do everything you want. There is one unlabeled button, the first element on the screen, that is an info button for options to send email feedback or access the developer's web site. Accessibility of the various financial calculators was very good, except for the generic calculator, whose buttons were labeled by column and row position instead of functions. You'll want to use the default iPhone calculator instead.
When you launch the app you are on a screen with heading "Financial Calculators" that lists different types of Financial Calculators you can select. Flick through the list to the fourth entry, which is "Compound Interest Calculator", and double tap. The format of the calculator template is to list items with corresponding text fields that you fill in, along with buttons to "reset", "calculate", or for options to be set, such as the compounding method (set to "monthly" by default, but double tap to select other options). The onboard keyboard that comes up in the bottom half of the screen for text entry is similar to the dial pad for the phone: there's a nine-pack of numbers 1 thourgh 9 in the first three rows, and the bottom (4th) row has the period, "0", and delete key in the bottom right corner. The input key action can be set to either standard typing or touch typing by setting the rotor to "Typing Mode".
So, for example, you'd enter the "Principal Amount", "Monthly Deposit", "Period" of your calculation (in months), and "Annual Interest Rate %" into the text fields, optionally change the compounding method by double tapping the "Monthly" button, then double tap the "Calculate" button that is below the "monthly" button and just above the "3" key of the onboard keyboard. The onboard keyboard will disappear, and if you flick right you will be able to read the interest amount and maturity value. Further flicking right gives access to an "Email" button, that allows you to send the results of your computation, and an "Interest Table" button that accesses a screen which lists a table with 3 columns for the months, interest, and balance for the period of your term calculation. Double tap the "Back" button in the top left corner to return to your "Compound Interest Calculator" screen, and then double tap the "Home" back button in the top left corner to return to the home screen with the list of financial calculators.
There are a large number of financial calculators listed, so you will want to use the "Edit" button in the top right corner of the screen to reorder the list so that the calculators you most frequently use appear first. Double tap the "Edit" button, then flick right to the calculator you want to list first (e.g., the compund interest calculator). Following each listed financial calculator, there witll be a button along the right edge of the screen to reorder the position of that calculator. VoiceOver will say, for example, "Reorder Compound Interest Calculator, button, draggable; double tap and hold, wait for the sound, then drag to rearrange." When focus is on that button you can do a double tap and hold gesture anywhere on the screen. Without lifting your finger from the screen, move it up. You'll hear a plinking sound as you pass the previous entry, and VoiceOver will announce "moved above Loan Calculator", or whichever entry you pass. While in editing mode, you can flick to any other calculator, flick right to its reorder button, double tap and hold, then move that calculator up in position. For example, you might want to do this for the "ROI Calculator" that lets you calculate a general return on investment, or for the "Loan Calculator". When you have finished rearranging the order of your calculators by dragging them into position, double tap the "Done" button in the top right corner of the screen.
There are separate calculators for auto loans, auto lease, retirement/401km abd credit card payoffs. On a quick check, all of these seem to be accessible and use the dial-pad-like onboard keyboard for input. The one exception to using this keyboard is the "TVM (Time Value of Money) Calculator", that is the first of the listed calculators on the home screen, and which is the most complicated of the calculators to use. This calculator uses the "more numbers" keyboard for general text entry, and also has a separate button for "Instructions" that I had to read just to figure out what the input variables and terminology were. This calculator is also accessible, but is more complex in its setup and button options. It's also the only one of the calculators with a separate button for instructions -- the others are self-explanatory. Had I stopped my examination of the app with this calculator, which is the first of the listed financial calculators, I would have judged this app to be far more difficult to use than it is. That's another reason for reordering the list of calculators to put this closer to the end. You may also want to use the option to custom relabel the names of the calculators with a two-finger double tap and hold. Wait for the tri-tone sound and then edit the text field for the label element. For acronyms like the "ROI Calculator" I changed the label to insert spaces between the letters "R O I" so that VoiceOver pronounces each letter instead of trying to pronounce the word "roi", which it mumbles indistinctly. I don't have a problem with the pronunciation of the "APR Calculator" as "April Calculator", but if you want to relabel this by putting spaces between the letters "A P R", you can perform the same relabeling trick.
The only listed calculator with problems is the generic "Calculator" that is included in the list, since the buttons are announced with labels like "42 0" instead of "7", etc. Just use the default calculator on your iPhone instead. You can also use Siri to do some of these calculations. This set of financial calculators work by template screens with text fields for selected parameters. You can either clear all fields with the "reset" button, or modify the text fields of just the values you want to change and double tap the "calculate" button again. Then you can use the "email" button to mail a summary of the calculation.
I'll append the list of calculators from the app description:
The widely popular, easy to use and feature rich financial calculators app comes to iPhone/iPad:
* TVM Calculator
* Currency Converter
* Loan Calculator
* Compound Interest Calculator
* Retirement/401k Calculator
* Credit Card Pay Off Calculator
* Tip Calculator
* Annual Percentage Rate (APR) Calculator
* Return on Investment (ROI) Calculator
* Auto Loan Calculator
* Auto Lease Calculator
* IRR NPV Calculator
* Calculator and Unit Conversion
* Percentage Calculator
For TVM calculator, there are buttons PV, PMT, FV, Rate, and Periods on the right hand side. If you want to calculate Future Value, for example, click FV button.
Here is the link for an accessible HP 12C. This does all financial calculations.