task_4_exam

get r in secant methods

//  main.cpp
//  exam_4
//
//  Created by Nanxing LAI on 2019/1/19.
//  Copyright © 2019 Mac. All rights reserved.

//





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


using namespace std;

//the check of interger number, only for the number of periods
int inputInteger(string prompt){
    cout << prompt;
    int n;
    cin >> n;
    
    while(n < 1){
        cout << "invalid, " << prompt;
        cin >> n;
    }
    return n;
}

// the test of double value number, which inluding r, pmt and pv
double inputDouble(string prompt){
    cout << prompt;
    double value;
    cin >> value;
    
    while(value < 0){
        cout << "invalid, " << prompt;
        cin >> value;
    }
    return value;
}

// we use secant method in this task, so we need define the f function firstly, which value shoulb be zero.
double f(double r,double pmt, double pv, int n)
{
    
    return(pmt/pv-r*(1+1/(pow(1+r,n)-1)));
    
}

// we define the approximate pv satisfying the compounent interest formula: pmt*n=(1+r)^n*pv/n
// here we get the approximate function to calculate the PV
double approximateR(double pv, double pmt,int n)
{
    double k,g;
    k=n*pmt/pv;
    g=1.00/n;
    return(pow(k,g)-1);
    
}



int main()
{
    double r,rnext,pv,pmt,temp,a,b;
    int n;
    // providing values
    n = inputInteger("please input number of periods: ");
    pv = inputDouble("please input present value: ");
    pmt=inputDouble("please input the instalment:  ");
    
    r=approximateR(pv, pmt, n);// run the approximatePMT function above
    rnext=r*0.95;  //here we define the starting points
    
    a=f(r,pmt,pv,n);
    b=abs(a);
    
    
    while(b>0.0001) //loop ends once the error smaller than 0.01;
    {
        temp=rnext-f(rnext,pmt,pv,n)*(rnext-r)/(f(rnext,pmt,pv,n)-f(r,pmt,pv,n));
        r=rnext;
        rnext=temp;
        a=f(r,pmt,pv,n);
        b=abs(a);
        
    }
    
    
    
    cout<<"the r is "<<r<<endl;
    
    return 0;
}