Finance Calculator, home finance calculator.#Home #finance #calculator


home finance calculator

Home finance calculator

Version 4.5 2015.11.23

(double-click any word to see its definition)

Instructions: Type in four known values, then press one of the buttons at the right to compute the unknown value.

(to solve an example problem, press the “$fv$” button above)

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 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 the specified 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 per-period interest rate on the account.

These equations are similar to those used to calculate Population Increase , but they allow you to specify interest 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 (click here to test this result with the calculator above).

Equation List

Here are the equations for all the directly computable forms this problem can take, including the variations created by choosing payment-at-beginning and payment-at-end.

Payment at Beginning:

When using these equations, be sure 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negative values for owed balances and money paid into the account, positive values for balances in your favor and money withdrawn from the account. For these equations, enter percentages as ratios, thus 8% = 0.08 yes, the financial calculator at the top of the page accepts percentages as integers, but these equations are more portable and universal in part because they avoid certain kinds of hand-holdy conversions.

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 $np$, the computation will fail 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 banks use the procedure * it’s wise to go along, otherwise your numbers will not agree with those of the bank.

Interest rate ($ir$) computation: The case of $ir$ cannot be solved without iteration (using 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 the “$ir$” button again.

While reviewing the access logs for arachnoid.com, I noticed some visitors had been trying to specify values for Financial Calculator to save time when 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 in order to compute a payment amount:

If 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:

The basic URL syntax for using this feature looks like this:

Normally the calling parameters are added to the URL that identifies 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.

In a recent revision, to improve this page’s appearance and avoid the possibility of typographical errors I decided to automatically generate all the financial equation’s computable forms by deriving them from a canonical equation I wrote many years ago:

\begin fv\, = \frac<1> \left(pmt\, \left(ir\, pb\, + 1\right) – \left(ir\, + 1\right)^ \left(ir\, pb\, pmt\, + ir\, pv\, + pmt\,\right)\right) \end

Using the Python symbolic math library sympy, which over a period of years has become quite powerful, I set up a code block in which the above equation is solved for each of its computable variables (interest rate can’t be computed directly):

The idea of the LaTeX generator is that it exploits the existence of MathJax rendering support in this page to display the equations with little struggle or chance for errors.

This arrangement has a number of advantages, among which are a great reduction in effort, and a way to avoid the kinds of transcription errors that make online code listings so unreliable.

I also created numerical functions for each of the equation forms and tested them for consistency:

In the above test, I compute a payment amount for an ending balance of 100,000 after 200 payment periods. I then apply that payment amount to a round-robin in which a future value is computed, then that future value is applied to tbe problem of computing a present value for the same parameters. The results were:

The second value, which in principle should be zero, shows the effect of limited precision in computer numerical mathematics.

This programming effort honors the mathematical principle that applications of an established, reliable result should be derived carefully, with as little room for error as possible.

The full Python listing to generate the above results is located here.


Business News & Financial News, Reuters, home finance software.#Home #finance #software


Business

Home finance software

SoftBank says considering investment in Uber but no final agreement reached

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Asia stocks subdued as China data disappoints

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Shrinking GE rattles investors, shares hit 5-year low

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Silicon Valley blasts Senate proposal to tax startup options

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Roku hits record high on Philips licensing deal

Goldman Sachs marks stake in Weinstein Co down to zero: source

Tesla hit by class-action lawsuit claiming racial discrimination

Wal-Mart partners with Lord & Taylor to expand online fashion presence

Emirates believes Airbus can guarantee development of A380 program

Qualcomm rejects Broadcom’s $103-billion takeover bid

Business Video

GE’s turnaround plan met with investor slap down

GE to focus on 3 businesses

Wall Street ticks higher

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*All quotes delayed a minimum of 15 minutes. See here for a complete list of exchanges and delays.


Personal Finance Software – Quicken Alternative, home finance software.#Home #finance #software


Personal Finance Software for Mac OS X or Windows

AceMoney is the best Quicken or Microsoft Money alternative financial software you can find, for Mac OS X or Windows. Manage accounts of different types in different currencies, track your spending habits, record your expenses, or do on-line banking. You do not have to be an accountant to use it. It is so easy! Set your mind at ease by scheduling automatic backup.

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When it comes to keeping track of your finances, AceMoney personal finance software is extremely easy to navigate and offers several important features, such as the ability to manage your mortgage, view your spending habits and see your current cash flow. Having these options will help you get a full picture of your personal finances and help you arrive at your long-term goals.

The program’s interface is very businesslike, and its simple, straightforward design makes the array of options easy to understand and navigate. Large commands at the top of the window let you toggle between seven categories, including accounts, portfolio, banks, payees, and reports.

Some free financial tools come as big files but AM Lite is an exception, and it’s very quick to install, too. The interface is a model of simplicity, and is much less cluttered than Microsoft Money or Quicken. All commands can be accessed via both buttons and menus and the software is aimed at small business, as well as personal users.

Microsoft Money users will feel somewhat at home with AceMoney. The software uses the same browser-like navigation Money users got used to. It’s pretty stripped down, but handles the basics.

Bottom line – Comprehensive but simpler to use than Quicken or Money.

Useful Links

  • AceMoney Questions

and Answers

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    at Yahoo

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    Personal Finance Software – AceMoney

    Home finance softwareUsing AceMoney, personal finance software for Mac OS X or Windows, to organize your personal finances is quick and easy. All the features expected from home budget or even small-business accounting software are supported.

    Multiple account management

    AceMoney, personal finance software, supports different account types like checking, savings, credit cards, loans, debt accounts. You can even create your own custom account type!

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    AM, personal finance software, can be configured to automatically download transactions from your bank, categorize them, and give you an updated balance of your home budget.

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    There are more than 100 existing spending categories. Configure your home budget limits for every category and track the difference between actual and budgeted values.

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    All your business and personal transactions are automatically categorized by AM, personal finance software, so you can see exactly where your money i spent. You can generate home budget reports by categories or payors/payees. See how much you spent on food last month. Find any transactions by any parameter.

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    AM, personal financial software for Mac OS X or Windows, requires only 8 megabytes of memory.

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    Quicken Alternative / Microsoft Money Alternative

    AceMoney is an award-winning, Microsoft Money and Quicken personal finance software alternative

    Many of our customers have been long time Microsoft Money or Quicken users, but made a switch after learning and appreciating the simplicity and ease of use of AceMoney, personal financial software. You can start managing your home budget right away, you do not have to be a finance expert.

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    You can easily transfer years of existing transactions: Microsoft Money Alternative or Quicken Alternative. AceMoney can also import your data from other personal finance software in the industry standard QIF and OFX formats. AceMoney is an award-winning Quicken alternative!

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    All over the world, AceMoney, personal financial software, is loved by people for satisfying their personal needs. Read testimonials from our customers.


  • Repco batteries, rebranded century? Servicing, repco home finance.#Repco #home #finance


    Whirlpool

    hey guys, went into repco today to get what i was lead to believe a century ultra hi performance battery, n70zz4wd specifically. get in there to find out it’s repco branded, i’m like you said it was century. oh this is a century just has our sticker on it. and it turned out they didn’t have the right battery anyway it was a L terminal on the opposite side, but could get the right one in tomorrow.

    anyway, main reason i went there was cause they have the 20% off this month for racq, so the $229 battery was like $45 off.

    so my question really is, are the repco batteries true century, are they as good, or are they just a generic not as good materials used in them, dud/failed century batteries if you get where i’m coming from.

    If its not one of the cheaper ones they sell it is indeed a re badged century battery.

    I’ve used Repco branded batteries in my vehicles for a few years now without issue.

    Sorry to disappoint you but that discount does not apply to batteries.

    ^20% off applies to full retail price and cannot be used in conjunction with any other offer or discount. Discount does not apply to purchases of car navigation devices, motor vehicle and marine batteries, engines, gift cards, any trade purchases and Trade Workshop Equipment. Store stock only. Must present RACQ Membership card to claim discount. Offer valid 1-31 July 2013.

    well considering that, the repco guy even knew i had a racq card and was like yea it’s fine. think i’ll just get a genuine century from batteryworld and be done with it

    Just grabbed one of these, and although the sign said not on Car or marine, when i asked the guy at the checkout he said, offcourse on batteries as well. 25% off, i ended up paying $114 for the High performance battery. Yes they are rebranded Century Yuasa. 24 months warranty, not bad.

    they are also quite good value. My VZ cost about $155.

    just got one for the vy at the 25% off :), ended up getting a genuine century for the pajero, but thought might as well, it’s battery is a good 6 years old, still starting, but probably wont last much longer

    vxcalais01, does your battery have a manufacturing stamp on it. the only thing i can see on mine is on the body D9HG, and if the D9 is it, then it’s a 2009 battery, which is not good.


    Cumming, GA Payroll and HR Outsourcing Firm, Home Page, Reliance Payroll, LLC, reliance home finance.#Reliance #home #finance


    Welcome to our Payroll and HR Outsourcing firm in Cumming, GA.

    We offer payroll solutions that meet your business’s needs and enable you to spend time doing what you do best- -running your company. Read more.

    Payroll direct deposit is a convenient and safe way to electronically pay your employees on payday. Direct deposit service is safe, fast, and easy – plus, it saves your company time and money! Read more.

    It’s critical for any company to attract and keep talented employees. We set up and administer 401K and SIMPLE IRAs to help you achieve greater stability for your company, while helping your employees meet their long-term financial goals for retirement. Read more.

    Outsourcing health benefits administration can result in reduced costs, compliance and improvd employee engagement. With the advent of healthcare reform, Reliance Payroll can help you make informed decisions and chart the smartest course. Read more.

    Reliance Payroll administers workers’ compensation insurance and related programs (management of claims, injury reporting, back to work programs, etc.). We help develop safety programs for its clients and assist with OSHA record keeping requirements. Read more.

    Employees enjoy extra spending money per paycheck while they save on out-of-pocket expenses like doctor and dentist co-pays, prescriptions, and day-care costs with a Flexible Spending Account (FSA) set up by Reliance Payroll. Read more.

    Hiring a payroll service is a very important decision. You need to partner with an organization you can trust. We’ll help you begin making an informed decision with this FAQ list.Read more.

    If you’re a small-business owner, you know the frustration of spending more time than you want or should on non-revenue-generating activities. From payroll and human resource management to benefits and compen- sation, entrepreneurs can spend up to 40% of their precious day engaged in these necessary but time-sucking tasks. We can help.Read more.

    We help businesses make safe and informed decisions by providing employment, business, and tenant screening, as well as drug testing and investigative services.Read more.

    Consider how much recruiting, employee turnover and “bad-hires” cost your business each year. Have you hiring the best possible candidates? Have you hired someone during the last year that turned out to be a criminal and/or a drug addict? Reliance Payroll has the expertise to help ensure efficient and effective hiring, as well successfully conducting new employee orientation.Read more.

    We can your help business manage employee performance and development. By developing and implementing performance management plans. we help ensure employees comply with company policies and procedures and successfully meet business goals. We can also periodically monitor employee performance and report findings to management. This reduces the workload of managers by minimizing the amount of administrative responsibilities they must focus on.Read more.

    Because we’re well-versed in developing handbooks, Reliance Payroll is also uniquely qualified to help you articulate your company’s policies. And that enables you to handle issues deftly before they ever arise, such as use of company property, alcohol/drug use, anti-compete clauses, commissions, etc. Read more.


    Reliance Home Finance debuts at Rs 107 on NSE, business-news, Hindustan Times, reliance home finance.#Reliance #home #finance


    Reliance Home Finance debuts at Rs 107 on NSE

    Reliance home finance

    Updated: Sep 22, 2017 11:19 IST

    By Indo Asian News Service , Indo Asian News Service

    Housing finance company Reliance Home Finance Ltd (RHFL) — part of Anil D Ambani-led Reliance Group — on Friday debuted on the NSE at Rs 107.20.

    Tina Ambani, wife of Anil Ambani, rang the bell signaling the listing of RHFL on the NSE.

    Anil Ambani, Chairman, Reliance Group of Companies was also present at the event.

    Speaking at the listing function Anmol Ambani, Executive Director, Reliance Capital Ltd said: The listing results in Reliance Capital shareholders directly owning stake in RHFL, with over nine lakh shareholders, the largest shareholder base in a housing finance company.

    Referring to Prime Minister Narendra Modi s vision for Housing for All he said: Our focus remains on affordable housing and you will see proportion of that increasing in our overall book.

    Reliance Capital holds 51 per cent in Reliance Home Finance.

    We are delighted to have achieved this milestone in such a short period of time. But none of this would have been possible without the continued support of the strong team at RHF and our 33,000 customers, who have shown faith towards the Company and have allowed us to serve them, Ravindra Sudhalkar, Executive Director and CEO of RHFL said.

    All Shareholders of Reliance Capital Ltd. have already received one free share of RHFL for every share held in Reliance Capital Ltd. as on Record Date i.e. September 6, 2017, Reliance Capital had said earlier in a statement.

    Reliance Home Finance has assets under management (including securitised portfolio) of Rs 13,022 crore ($2 billion) as of June 30, 2017.


    Andhra Bank Home Loan, Interest Rates, Eligibility – Deal4loans, repco home finance.#Repco #home #finance


    Andhra Bank Home Loan |Interest Rates | Eligibility

    Andhra Bank home loans Find details on Documents, processing fees, approval, loan amount, eligibility, lowest emi.

    Andhra Bank is a medium-sized public sector bank, with a network of 2507 branches, 15 extension counters, 38 satellite offices and 2232 automated teller machines as on 31 Mar 2015 and planning to open 300+ branches by 31 March 2016.

    Andhra Bank home loan emi calculator

    Eligibility of loan amount is based on repayment capacity.

    1. the plot is to be situated in residential areas within Municipal/Corporation limits in urban and metro areas.

    2. Finance shall also be considered for purchase of sites offered for sale by state owned agencies like Housing Boards etc. in urban and metro areas

    3. Maximum time limit to complete construction of house stipulated is 12 months from the date of loan for purchase of plot. Failure to comply with will result in declassifying the account from housing loans and charging commercial rate of interest.

    4. Assessment of eligible amount of loan is is based on repayment capacity for both the components of loan – i.e. for plot and construction together.

    ✓ Agreement for sale between vendor and purchaser.

    ✓ Name and address of the vendor and purchaser.

    ✓ Copies of link documents of title to the property in possession of the vendor along with tax receipts.

    ✓ Original receipts for payment s made to builder/vendor.

    ✓ Copy of the approved plan.

    ✓ Certificate from Approved Engineer about the present value, condition and life of the house/flat.

    ✓ Lay out approval.

    ✓ Copy of approved plan.

    ✓ Detailed estimate of construction.

    ✓ Original title deeds of the site.

    ✓ Development Agreement between the owner of the site and builder.

    ✓ Allotment letter of the house / flat issued by Housing Board.

    ✓ NIL Encumbrance Certificate.

    ✓ Any other document stipulated by Legal Advisor / Sanctioning authority.

    ✓ 0.50 % of loan amount subject to maximum of Rs.10000/- + applicable tax.

    ✓ No prepayment charges for loans with floating rate of interest

    ✓ For loans up to Rs.10.00 lacs – Rs.100 per quarter.

    ✓ For loans above 10 .00 lacs to 15.00 lacs Rs.150 per quarter

    ✓ For loans above Rs.15.00 lacs Rs.250 per quarter.

    Other products of Andhra Bank are:


    Sundaram Select Midcap Fund – Regular Plan: Fund Snapshot: Sundaram Mutual Fund – Value Research Online, sundaram home finance.#Sundaram #home #finance


    Sundaram Select Midcap Fund – Regular Plan Sundaram home finance

    • Growth: R 507.1383
    • Dividend: R 42.6704
    • NAV of Other Plans

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    Sundaram home financeIndicates a new holding since last portfolio

    • Fund News: Sundaram Mutual Fund announces dividend | Jan 16, 2017
    • Fund News: Sundaram Select Midcap Fund announces dividend at Re 1 per unit | Oct 07, 2014
    • Interview: Economy Poised to Grow at 7% | Aug 26, 2014
    • Fund News: Sundaram Select Midcap Fund declares dividend | Oct 21, 2013
    • Fund Family Update: Niche Offerings | Jan 03, 2013
    • Fund News: 20% Dividend in Sundaram Select Mid Cap Fund | Nov 08, 2010
    • Fundwire: Diversified equity funds cross Jan �08 NAV levels | Sep 21, 2010
    • Fund News: 15% Dividend under Sundaram BNP Paribas Select Midcap | Feb 04, 2010
    • Fund News: Sundaram BNP Paribas Select Midcap: Dividend Declaration @ 15% | Feb 01, 2010
    • Fund News: 15% Dividend under Sundaram BNP Paribas Select Mid Cap | Nov 16, 2009
    • More news and analysis on this fund

    Address: Sundaram Towers, 2nd Floor, 46, Whites Road, Royapettah Chennai – 600014 | Phone: (044) 28583362/ 28583367/ 28569900/1800 103 7237 | Fax: (044) 28583156

    Registrar & Transfer Agent: Sundaram BNP Paribas Fund Services

    Address: No. 23, Cathedral Garden Road Nungambakkam Chennai – 600034


    Finance Calculator, home finance calculator.#Home #finance #calculator


    home finance calculator

    Home finance calculator

    Version 4.5 2015.11.23

    (double-click any word to see its definition)

    Instructions: Type in four known values, then press one of the buttons at the right to compute the unknown value.

    (to solve an example problem, press the “$fv$” button above)

    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 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 the specified 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 per-period interest rate on the account.

    These equations are similar to those used to calculate Population Increase , but they allow you to specify interest 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 (click here to test this result with the calculator above).

    Equation List

    Here are the equations for all the directly computable forms this problem can take, including the variations created by choosing payment-at-beginning and payment-at-end.

    Payment at Beginning:

    When using these equations, be sure 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. For these equations, enter percentages as ratios, thus 8% = 0.08 yes, the financial calculator at the top of the page accepts percentages as integers, but these equations are more portable and universal in part because they avoid certain kinds of hand-holdy conversions.

    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 $np$, the computation will fail 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 banks use the procedure * it’s wise to go along, otherwise your numbers will not agree with those of the bank.

    Interest rate ($ir$) computation: The case of $ir$ cannot be solved without iteration (using 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 the “$ir$” button again.

    While reviewing the access logs for arachnoid.com, I noticed some visitors had been trying to specify values for Financial Calculator to save time when 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 in order to compute a payment amount:

    If 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:

    The basic URL syntax for using this feature looks like this:

    Normally the calling parameters are added to the URL that identifies 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.

    In a recent revision, to improve this page’s appearance and avoid the possibility of typographical errors I decided to automatically generate all the financial equation’s computable forms by deriving them from a canonical equation I wrote many years ago:

    \begin fv\, = \frac<1> \left(pmt\, \left(ir\, pb\, + 1\right) – \left(ir\, + 1\right)^ \left(ir\, pb\, pmt\, + ir\, pv\, + pmt\,\right)\right) \end

    Using the Python symbolic math library sympy, which over a period of years has become quite powerful, I set up a code block in which the above equation is solved for each of its computable variables (interest rate can’t be computed directly):

    The idea of the LaTeX generator is that it exploits the existence of MathJax rendering support in this page to display the equations with little struggle or chance for errors.

    This arrangement has a number of advantages, among which are a great reduction in effort, and a way to avoid the kinds of transcription errors that make online code listings so unreliable.

    I also created numerical functions for each of the equation forms and tested them for consistency:

    In the above test, I compute a payment amount for an ending balance of 100,000 after 200 payment periods. I then apply that payment amount to a round-robin in which a future value is computed, then that future value is applied to tbe problem of computing a present value for the same parameters. The results were:

    The second value, which in principle should be zero, shows the effect of limited precision in computer numerical mathematics.

    This programming effort honors the mathematical principle that applications of an established, reliable result should be derived carefully, with as little room for error as possible.

    The full Python listing to generate the above results is located here.