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I need a javascript formula that calculates daily, weekly, monthly compound interest accurately

Posted on 2009-04-09
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Last Modified: 2012-05-06
I need a very accurate calculator formula, right now my formula works for monthly contributions with monthly compounding, but when you use weekly contributions with monthly compounding, I don't know how to adjust the formula. You can see my calculator in action at by downloading and unzipping the attached files.

So far, this is the most accurate calculator I've found on the web (I'd be happy if you could get a javascript formula to match the values generated by this calculator):
http://tiny.cc/kmhGP

Here is the problem with weekly contributions and monthly compounding:
1. there are 52 weeks in a year, but some months have 5 weeks while others have 4, however I don't think their calc takes this into account, I think they simply base their calculation on 52 weeks and every 4 weeks they compound the interest.

Anyway, here is the formula I'm using:

var P = startingAmount;
    var Y = yearsOfInvesting;
    var c = getAdditionalContributionsPerPeriod;
    var t = getTermsPerPeriod;
    var n = t * Y;
    var r = interestRate / 100 / t; // interestRate [%]
    var z = 1 + r;
 total = P * Math.pow(z, n) + c * (Math.pow(z, n + 1) - z) / r;

For a scenario:
1. $1000 principal
2. $50 per week contribution
3. 10 years
4. monthly compounding
The total according to: http://tiny.cc/kmhGP should be $30,007 rounding the decimals up.

The closest I've come to this is by this formula is by weekly contributions & weekly compounding (but I want to change it to monthly compounding):
<script>
var P = 1000;//startingAmount;
    var Y = 0;//yearsOfInvesting;
    var c = 50;//
    var n = 520;//t * Y;
    var r = .02/52;
    var z = 1 + r;

mz=  P * Math.pow(z, n) + c * (Math.pow(z, n + 1) - z) / r;
document.write(mz);
</script>
How can I make my formula work for weekly and daily contributions?
 
// Savings calculator formulas
 
// Parameters:
//startingAmount
//years
//additionalContributions
//interestRate
//aditionalContributionsPeriod: 1 - per week; 2 - bi-weekly; 3 - per month; 4 - per quarter; 5 - per year
//interestRatePeriod, Compound: 1 - Daily; 2 - monthly; 3 - quarterly; 4 - annually
 
 
function getDataForChart(startingAmount, yearsOfInvesting, additionalContributions, interestRate, 
    aditionalContributionsPeriod, interestRatePeriod) {
   // Map to one - letter variables
   //var P = startingAmount;
   var Y = yearsOfInvesting;
  // var c = getAdditionalContributionsPerPeriod(startingAmount, yearsOfInvesting, 
      // additionalContributions, interestRate, aditionalContributionsPeriod, interestRatePeriod);
  // var t = getTermsPerPeriod(startingAmount, yearsOfInvesting, 
      // additionalContributions, interestRate, aditionalContributionsPeriod, interestRatePeriod);
  // var n = t * Y;
  // var r = interestRate / 100 / t; // interestRate [%]
  // var z = 1 + r;
   
   var data1 = new Array();
   var data2 = new Array();
   for (var i = 1; i <= Y; i++) {
       // Base amount:
       var B = calculatePrincipal(startingAmount, i, additionalContributions, interestRate, 
                 aditionalContributionsPeriod, interestRatePeriod);
       data1[i - 1] = [i, B];
       // Compound contributions:
       var Cc = calculateTotal(startingAmount, i, additionalContributions, interestRate, 
                aditionalContributionsPeriod, interestRatePeriod);
       // var Cc = P * Math.pow(z, i) + c * (Math.pow(z, i + 1) - z) / r;
       data2[i - 1] = [i, Cc];
   } 
   
   var series = new Array();
   series[0] = data1;
   series[1] = data2;
   return series;
}
 
function calculatePrincipal(startingAmount, yearsOfInvesting, additionalContributions, interestRate, 
    aditionalContributionsPeriod, interestRatePeriod) {
   
    var P = startingAmount;
    var Y = yearsOfInvesting;
    var c = getAdditionalContributionsPerPeriod(startingAmount, yearsOfInvesting, 
       additionalContributions, interestRate, aditionalContributionsPeriod, interestRatePeriod);
    var t = getTermsPerPeriod(startingAmount, yearsOfInvesting, 
       additionalContributions, interestRate, aditionalContributionsPeriod, interestRatePeriod);
    var n = t * Y;
    var r = interestRate / 100 / t; // interestRate [%]
    var z = 1 + r;
    var coeff = 1;
    if (aditionalContributionsPeriod == 1) {
	coeff = 52;
    }
    else if (aditionalContributionsPeriod == 2) {
	coeff = 26;
    }
    else if (aditionalContributionsPeriod == 3) {
	coeff = 12;
    }
    else if (aditionalContributionsPeriod == 4) {
	coeff = 4;
    }
    return startingAmount + coeff * additionalContributions * yearsOfInvesting;
}
 
function calculateTotal(startingAmount, yearsOfInvesting, additionalContributions, interestRate, 
    aditionalContributionsPeriod, interestRatePeriod) {
    
    var P = startingAmount;
    var Y = yearsOfInvesting;
    var c = getAdditionalContributionsPerPeriod(startingAmount, yearsOfInvesting, 
       additionalContributions, interestRate, aditionalContributionsPeriod, interestRatePeriod);
    var t = getTermsPerPeriod(startingAmount, yearsOfInvesting, 
       additionalContributions, interestRate, aditionalContributionsPeriod, interestRatePeriod);
    var n = t * Y;
    var r = interestRate / 100 / t; // interestRate [%]
    var z = 1 + r;
    return P * Math.pow(z, n) + c * (Math.pow(z, n + 1) - z) / r;
}
 
function getTermsPerPeriod(startingAmount, yearsOfInvesting, additionalContributions, interestRate, 
      aditionalContributionsPeriod, interestRatePeriod) {	
  
      if (interestRatePeriod == 1) {
	  return 365;
      }
      else if (interestRatePeriod == 2) {
	  return 12;
      }
      else if (interestRatePeriod == 3) {
	  return 4;
      }
      else {
	  return 1;
      }
      return 1;
}
 
function getAdditionalContributionsPerPeriod(startingAmount, yearsOfInvesting, 
    additionalContributions, interestRate, aditionalContributionsPeriod, interestRatePeriod) {
  
  var divideFactor = 1;
  if (interestRatePeriod == 1) {
      // Additional contributions per day
      if (aditionalContributionsPeriod == 1) {
	  // Week => factor = 7
          divideFactor = 7;
      }
      else if (aditionalContributionsPeriod == 2) {
	  // Biweekly => factor = 14
          divideFactor = 7;
      }
      else if (aditionalContributionsPeriod == 3) {
	  // Monthly => factor = 30
          divideFactor = 30;
      }
      else if (aditionalContributionsPeriod == 4) {
	  // Per quarter => factor = 91
          divideFactor = 91;
      }
      else if (aditionalContributionsPeriod == 5) {
	  // Per year => factor = 365
          divideFactor = 365;
      }
  } 
  else if (interestRatePeriod == 2) {
      // Additional contributions per month
      if (aditionalContributionsPeriod == 1) {
	  // Week
          divideFactor = 1 / 4;
      }
      else if (aditionalContributionsPeriod == 2) {
	  // Biweekly
          divideFactor = 1 / 2;
      }
      else if (aditionalContributionsPeriod == 3) {
	  // Monthly
          divideFactor = 1;
      }
      else if (aditionalContributionsPeriod == 4) {
	  // Per quarter
          divideFactor = 4;
      }
      else if (aditionalContributionsPeriod == 5) {
	  // Per year
          divideFactor = 12;
      }
  }   
  else if (interestRatePeriod == 3) {
      // Additional contributions per quarter
      if (aditionalContributionsPeriod == 1) {
	  // Week
          divideFactor = 1 / 13;
      }
      else if (aditionalContributionsPeriod == 2) {
	  // Biweekly
          divideFactor = 1 / 6.5;
      }
      else if (aditionalContributionsPeriod == 3) {
	  // Monthly
          divideFactor = 1 / 4;
      }
      else if (aditionalContributionsPeriod == 4) {
	  // Per quarter
          divideFactor = 1;
      }
      else if (aditionalContributionsPeriod == 5) {
	  // Per year
          divideFactor = 4;
      }
  }   
  else if (interestRatePeriod == 4) {
      // Additional contributions per year
      if (aditionalContributionsPeriod == 1) {
	  // Week
          divideFactor = 1 / 52;
      }
      else if (aditionalContributionsPeriod == 2) {
	  // Biweekly
          divideFactor = 1 / 26;
      }
      else if (aditionalContributionsPeriod == 3) {
	  // Monthly
          divideFactor = 1 / 12;
      }
      else if (aditionalContributionsPeriod == 4) {
	  // Per quarter 
          divideFactor = 1 / 4;
      }
      else if (aditionalContributionsPeriod == 5) {
	  // Per year
          divideFactor = 1;
      }
  }   
  return additionalContributions / divideFactor;
}

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Question by:selpmet
  • 2
5 Comments
 
LVL 6

Accepted Solution

by:
mudbuggle earned 500 total points
ID: 24114910
To determine whether or not the month has 4 weeks or 5 weeks we need to determine the last day of the month. Here is an article on how to do that.
http://javascript.about.com/library/bllday.htm

Then you'll want to divide the last day of month by 7, then round up. Then multiply your total per week by the resulting number of weeks. If you want to calculate only on weeks that have weekendings in that month then you'll want to insert an if statement to verify that the last day of the month is on the last day of the week. I have an exampe below.
var dim = days in month;
var eomform = month + '/' + dim + '/'+ year
var eomdate = new Date(eomform);
var eomeow = eomdate.getDay();
if(eommeow == 6)
{
   var multiplier = whater var you set the calculated # of weeks to;
}
else
{
   var multiplier = whater var you set the calculated # of weeks to -1;
}

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Author Comment

by:selpmet
ID: 24116246
I don't understand the var multiplier - for instance 10 years would be 520 weeks and you're saying to subtract 1 from it?

Also, can you help me figure out the formula for calculating daily/monthly/quarterly/annually compound interest for weekly/daily/bi-weekly/monthly/annually made contributions? There has to be a financial math javascript library that already can do this like excel has.
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LVL 6

Expert Comment

by:mudbuggle
ID: 24116522
the multiplier is for on a monthly basis it will calculate per month... as I wrote it it would work for 1 month. Turns out I misread what you were asking, that was my fault. I can come up with something it will take a little though.
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LVL 16

Expert Comment

by:CWS (haripriya)
ID: 37169587
This question has been classified as abandoned and is closed as part of the Cleanup Program. See the recommendation for more details.
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