Question

Using Java:

When buying a house or condo (using a mortgage), or when taking out a loan, you’ll usually wind up with some form of a fixed monthly payment. Mortgages and loans work this way:

• You take out a loan from the bank or lender for
  • a specified amount of money
  • at a specified annual interest rate
  • with a specified monthly payment amount
• At the beginning of every month, interest is added to the amount you owe the bank or lender (the outstanding balance of your mortgage or loan)
• The amount you owe is then decreased by the your monthly payment to arrive at your new outstanding balance for the next month
• You continue to pay the bank or lender in monthly installments until the outstanding balance is paid in full (i.e., goes down to zero)

The numbers determined at the beginning of every mortgage or loan are:

• The original amount of the mortgage or loan
• The annual interest rate for the life of the mortgage or loan
• The monthly payment you’ll make until the outstanding balance is paid in full

Interest and new outstanding balance are calculated at the beginning of every month:

• monthly interest = (annual interest rate) / 12 * current outstanding balance
• new outstanding balance = current outstanding balance + monthly interest – monthly payment

If the new outstanding balance goes negative, then the over-payment for the last month is refunded and the mortgage is considered “paid in full”.

Write a program which uses a recursive method to determine and display the number of months required to pay off a mortgage or loan (when the new outstanding balance goes to 0.00) and the total interest paid over the life of the mortgage or loan. You may want to display the outstanding balance and monthly interest calculated at the beginning of each month, but this is not required.

Use the following test cases:

1. Initial loan: $180,000, annual interest: 6.25%, monthly payment: $1,850.00
2. Initial loan: $400,000, annual interest: 5.00%, monthly payment: $2,000.00

We also need to cover the case where the monthly payment amount doesn’t cover the calculated monthly interest. In this case, the balance on the loan actually goes up, not down! (This is known as “negative amortization”.) If this is the case, your recursive method should show the interest and the monthly payment for the first month, then stop.

Test case for negative amortization:

3. Initial mortgage: $300,000, annual interest: 4.50%, monthly payment: $1,000.00

Please print all dollar amounts to 2 decimal places.

Answer 1

All the explanation is in the code comments. Hope it helps!

Code:

import java.util.*;

public class Main
{
public static void calcInterest(float outBal, float annRate, float monthlyPay, int months, float totalInt)
{
// base condition
if(outBal <= 0)
{
// print the months and total interest
// months - 1 because the current months is not included
System.out.println("The number of months required to pay off a mortgage or loan: " + (months - 1));
System.out.printf("The total interest paid over the life of the mortgage or loan: $%.2f\n", totalInt);
return;
}
  
System.out.println("For month " + months + " ------------------------");
// print Outstanding balance
System.out.printf("Outstanding balance: $%.2f\n", outBal);
  
// calcuate monthly interest
float monthlyInterest = annRate / (100 * 12) * outBal;
  
// print monthly interest
System.out.printf("Monthly interest: $%.2f\n", monthlyInterest);
  
// check case of negative amortization
if(monthlyPay <= monthlyInterest)
{
System.out.println("Stopping because of negative amortization");
return;
}
  
// recursive call with updated Outstanding balance
calcInterest(outBal + monthlyInterest - monthlyPay,
annRate, monthlyPay, months+1, totalInt + monthlyInterest);
}
   public static void main(String[] args) {
       // input stream
       Scanner sc = new Scanner(System.in);
      
       float initLoan, annRate, monthlyPay;
      
       // input from user
       System.out.println("Enter initial loan, annual interest and monthly payment");
       initLoan = Float.parseFloat(sc.next());
       annRate = Float.parseFloat(sc.next());
       monthlyPay = Float.parseFloat(sc.next());
      
       // call to the recursive function with number of months as 1
       // and initial total interest as 0
       calcInterest(initLoan, annRate, monthlyPay, 1, 0.0f);
      
   }
}

Sample run:

Please note that the output was very long, therefore, given just a part of it.

#1

#2

#3

Code screenshots: