java compound interest with contributions formula

Question

I am currently trying to develop a compound interest calculator that includes monthly contributions. I have successfully been able to get the compound interest calculation working without the monthly contributions using the following line of code, but cannot figure out what the formula should be when adding monthly contributions.

double calculatedValue = (principalValue * Math.pow(1 + (interestRateValue/numberOfCompoundsValue), (termValue * numberOfCompoundsValue)));

When trying to get the calculated value with contributions I changed the way this is done. See the following code how I approached this.

//The starting principal
double principalValue = 5000;

//Interest rate (%)
double interestRateValue = 0.05;

//How many times a year to add interest
int numberOfCompoundsValue = 4;

//The number of years used for the calculation
double termValue = 30;

//The monthly contribution amount
double monthlyContributionsValue = 400;

//How often interest is added. E.g. Every 3 months if adding interest 4 times in a year
int interestAddedEveryXMonths = 12/numberOfCompoundsValue;

//The total number of months for the calculation
int totalNumberOfMonths = (int)(12 * termValue);

    for(int i = 1; i <= totalNumberOfMonths; i++)
    {

        principalValue += monthlyContributionsValue;

        if(i % interestAddedEveryXMonths == 0)
        {
            principalValue += (principalValue * interestRateValue);
        }
    }

I figured this should do what I am after. Every month increase the principal by the contribution amount and if that month equals a month where interest should be added then calculate the interest * the interest rate and add that to the principal.

When using the values above I expect the answer $355,242.18 but get $10511941.97, which looks better in my bank account but not in my calculation.

If anyone can offer me some help or point out where I have gone wrong that would be much appreciated.

Thanks in advance

Answer 1

static void Main(string[] args)
        {
            double monthlyDeposit;
            double rateOfInterest;
            double numberOfCompounds;
            double years;
            double futureValue = 0;
            double totalAmount = 0;
Console.WriteLine("Compound Interest Calculation based on monthly deposits");
            Console.WriteLine("Monthly Deposit");
            monthlyDeposit = Convert.ToDouble(Console.ReadLine());
            Console.WriteLine("Rate Of Interest");
            rateOfInterest = Convert.ToDouble(Console.ReadLine());
            Console.WriteLine("Number of Compounds in a year");
            numberOfCompounds = Convert.ToDouble(Console.ReadLine());
            Console.WriteLine("Number of year");
            years = Convert.ToDouble(Console.ReadLine());
            futureValue = monthlyDeposit;
            for (int i = 1; i <= years * 12; i++)
            {
                totalAmount = futureValue * (1 + (rateOfInterest / 100) / 12);
                if (i == years * 12)
                    futureValue = totalAmount;
                else
                    futureValue = totalAmount + monthlyDeposit;
            }
            Console.WriteLine("Future Value is=" + futureValue);
            Console.ReadLine();

        }

        //Output
        Compound Interest Calculation based on monthly Deposits
        Monthly Deposit
        1500
        Rate Of Interest
        7.5
        Number of Compounds in a year
        12
        Number of year
        1
        Future Value is=18748.2726237313

Answer 2

Your problem is here:

principalValue += (principalValue * interestRateValue);

You're adding a full year's interest every quarter, when you should be adding just a quarter's interest. You need to scale that interest rate down to get the right rate.

Here's an example:

class CashFlow {
    private final double initialDeposit;
    private final double rate;
    private final int years;
    private final double monthlyContribution;
    private final int interestFrequency;

    CashFlow(double initialDeposit, double rate, int years,
             double monthlyContribution, int interestFrequency) {
        if ( years < 1 ) {
            throw new IllegalArgumentException("years must be at least 1");
        }

        if ( rate <= 0 ) {
            throw new IllegalArgumentException("rate must be positive");
        }

        if ( 12 % interestFrequency != 0 ) {
            throw new IllegalArgumentException("frequency must divide 12");
        }

        this.initialDeposit = initialDeposit;
        this.rate = rate;
        this.years = years;
        this.monthlyContribution = monthlyContribution;
        this.interestFrequency = interestFrequency;
    }

    public double terminalValue() {
        final int interestPeriod = 12 / interestFrequency;
        final double pRate = Math.pow(1 + rate, 1.0 / interestPeriod) - 1;
        double value = initialDeposit;

        for ( int i = 0; i < years * 12; ++i ) {
            value += monthlyContribution;

            if ( i % interestFrequency == interestFrequency - 1 ) {
                value *= 1 + pRate;
            }  
        }

        return value;
    }
}

class CompoundCalc {

    public static void main(String[] args) {
        CashFlow cf = new CashFlow(5000, 0.05, 30, 400, 3);
        System.out.println("Terminal value: " + cf.terminalValue());
    }
}

with output:

run:
Terminal value: 350421.2302849443
BUILD SUCCESSFUL (total time: 0 seconds)

which is close to the $355k value you found.

There are a number of different conventions you could use to get the quarterly rate. Dividing the annual rate by 4 is a simple and practical one, but the pow(1 + rate, 1 / 4) - 1 method above is more theoretically sound, since it's mathematically equivalent to the corresponding annual rate.

Answer 3

After some brief testing I've come to the conclusion that either you have:

• miscalculated the value you want ($355,242.18)

  OR

• incorrectly asked your question

The calculation you've described that you want ($5000 start + $400 monthly contributions for 30 years + interest every 3 months) is found by the code you've provided. The value that it gives ($10,511,941.97) is indeed correct from what I can see. The only other suggestions I can offer are to only use double if you need to (for example termValue can be an int) AND when ever you know the value is not going to change (for example interestRateValue) use final. It will help avoid any unforeseen error in larger programs. I hope this helps you figure out your interest calculator or answers any questions you have.