/*
Program Written By Aaron J. Glover
Georgia Institute of Tehcnology
MS Quantiative & Computational Finance Program
Course: Math / ISYE 6767
Created Date: 2011-08-27
Revised Date: 2011-09-04
Version Number: 1.4
http://www.TheGlover.net
Aaron.Glover at GaTech.edu
Purpose: This program displays the future value of $1,000,000 by
using the inupts of annual interest rate and number of annual
compounding cycles per year.
*/
 
#include <iostream>  // for cout and cin
#include <iomanip>
#include <string>
#include <cmath> // access to aboslute value function
 
double e = 2.718281828459045235360287471352662497757247093699959574966;
 
using namespace std;
 
// Function uses loops to do a fast count from 1000s, then 10s, then 1s
 
int quickly_bound_value(double rate, double principal, double fv_target)
{
int n=1;
double value = (principal * pow( (1+(rate/n)),n));
for(n=1; value <= fv_target ; n=n+1000)
{
value = (principal * pow( (1+(rate/n)),n));
//    cout << "Iteration: " << n << " Value: " << value << endl;
}
 
n = n - 2001; // counter adjuster
value = 0;  // value reset
 
for(n=n; value <= fv_target ; n=n+10)
{
value = (principal * pow( (1+(rate/n)),n));
 
//   cout << "Iteration: " << n << " Value: " << value << endl;
}
 
n = n - 20; // counter adjuster
value = 0;
 
for(n=n; value <= fv_target ; n=n+1)
{
value = (principal * pow( (1+(rate/n)),n));
 
//    cout << "Iteration: " << n << " Value: " << value << endl;
}
n=n-1;  // counter adjuster
return n;
 
}
 
 
 
// Currency Formatting Function used from http://www.arachnoid.com/cpptutor/student3.html
void showCurrency(double dv, int width = 14)
{
 const string radix = ".";
 const string thousands = ",";
 const string unit = "$";
 unsigned long v = (unsigned long) ((dv * 100.0) + .5);
 string fmt,digit;
 int i = -2;
 do {
 if(i == 0) {
 fmt = radix + fmt;
 }
 if((i > 0) && (!(i % 3))) {
 fmt = thousands + fmt;
 }
 digit = (v % 10) + '0';
 fmt = digit + fmt;
 v /= 10;
 i++;
 }
 while((v) || (i < 1));
 cout << unit << setw(width) << fmt.c_str();
}
 
// Function calcualtes periodic compounding interest given inputs
double future_value(double rate, int frequency, double principal)
{
return (principal * pow(((rate/frequency) + 1),frequency));
}
 
// Function calculates numer of compounding cycles required to get within a specified amount of
// continiously compounded Future Falue
 
int find_compounding_cycles(double rate, double principal)
{
double fv_continious_compounding;       // variable to hold continiously compounded FV
double fv_target;                       // variable to hold target rate (cc rate - level of percision)
double precision = 0.005;               // difference between FV_cc and our target FV
 
fv_continious_compounding = principal * pow(e, rate);
fv_target = fv_continious_compounding - precision;
 
return quickly_bound_value(rate, principal, fv_target);
 
}
 
// Main Program | Returns the Value of $1,000,000 given interest rate and n periods
 
int main(){
double interest;                // variable to hold interest rate | ex: 12.00)
int frequency;                // variable to hold annual compounding persiods)
double principal = 1000000;     // variable to hold initial principal amount
 
cout << "\n";
cout << "\n";
cout << "\n";
cout << "****************************************************" << endl;
cout << "** Future Value of $1,000,000 after 1 year when   **" << endl;
cout << "** provided with annual interest rate and number  **" << endl;
cout << "** of compounding periods per year                **" << endl;
cout << "****************************************************" << endl;
cout << "\n";
cout << "Enter annual interest rate (in dec format): ";    // ex: 12.56 (percent) per year would be 0.1256
cin >> interest;
cout << "Enter number of annual compounding cycles: ";      // ex: 6
cin >> frequency;
cout << "\n";
// Display Current Formatted Result
cout << "Account Balance will be ";
showCurrency(future_value(interest, frequency, principal));
cout << " in 1 year" << endl;
cout << "\n";
cout.precision(0);
cout << "The number of compounding cycles required per year"<< endl;
cout << "to make the diffrence between the continiously compounded" << endl;
cout << "future-value and the periodic compounded future-value FV < 0.005: " << find_compounding_cycles(interest, principal) << endl;
cout << "\n";
}