#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

const int PAYMENTS_PER_YEAR = 12;

int main() {
    float principal,
          rate;

    int years,
        payments;

    float monthlyInterestRate,
          monthlyPayment;
  
    // print instructions
    cout << "This program will compute the monthly payments for a mortgate"
         << endl << endl;
	 
    // ask for parameters
    cout << "Enter the number of years => ";
    cin >> years;
    cout << "You will have the  loan for " << years << " years." << endl;
    cout << endl;

    cout << "Enter the amount borrowed (as a decimal number)  => ";
    cin >> principal;
    cout << fixed << setprecision(2);
    cout << "You borrowed $" << principal << endl;
    cout  << endl;

    cout << "Enter the interest rate (as a percent) => ";
    cin >> rate;
    cout << "Your interest rate is " << rate << "%, or " << rate/100.0 << endl;
    cout << endl;

    // Compute mortage
    // the monthly rate is used twice in the computation so do it early
    monthlyInterestRate = rate/(100.0 * PAYMENTS_PER_YEAR);

    // the exponent in the mortgage formula is the number of payments.
    payments = PAYMENTS_PER_YEAR * years;

    // this is the mortgage formula
    //                P r/n
    //    payment =  ------
    //               1-(1+r/n)^(-nt)
    
    monthlyPayment = monthlyInterestRate * principal
                  / (1 - pow((1 + monthlyInterestRate),-payments));

    // print the results
    cout << "Your monthly payments will be $" << monthlyPayment << endl;
 
    return 0;
}