Question

(In Java Using recursive techniques) When buying a house or condo (using a mortgage), or when taking out a loan, you’ll likely 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 overpayment 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

Remember to use Recursive techniques

Please print all dollar amounts to 2 decimal places.

Answer 1

import java.util.*;
class Main{
public static void main(String ar[]){
Scanner sc=new Scanner(System.in);
float principle,rate,monthlyPayment;
principle=sc.nextFloat();
rate=sc.nextFloat();
monthlyPayment=sc.nextFloat();
Loan l=new Loan(principle,rate,monthlyPayment);
l.print();
l.calculate();
}
}
class Loan{
private float principle;
private float rate;
private float monthlyPayment;
private float totalInterest;
private int time;
  
Loan(float principle,float rate,float monthlyPayment){
this.principle=principle;
this.rate=rate;
this.monthlyPayment=monthlyPayment;
}
public void print(){
System.out.println(principle);
System.out.println(rate);
System.out.println(monthlyPayment);
}
public void calculate(){
totalInterest=0;
time=0;
float x=principle*rate/1200; //interest of first month
//negative amortization if interest of first month>=monthly payment
if(x>=monthlyPayment){
System.out.print("Interest of first month is ");
System.out.printf("%.2f",x);
System.out.println();
System.out.print("Monthly payment is ");
System.out.printf("%.2f",monthlyPayment);
System.out.println();
}
// if it is positive amortization then
else{
calc(principle);
System.out.println("Time taken to pay the loan is "+time+" months");
System.out.print("Total interest paid is ");
System.out.printf("%.2f",totalInterest);
System.out.println();
}
}
private void calc(float amt){
if(amt<=0){ // if amount is <=0 then loan is paid fully
totalInterest=totalInterest-principle+amt; //Interest=paid money - (principle amount at the begining + overpayment(that will be refunded))
return;
}
amt=amt+amt*rate/1200-monthlyPayment; //principle amount for next month
time+=1; //no. of months passed till this point
totalInterest+=monthlyPayment; //paid money till now = money paid upto last month + payment of current month
calc(amt);
}
}