//10.11.js
// 2024-09-04
// $Id: 10.11.js 1.1 2024/11/03 06:30:00 s Exp $
//
// a : amount
// d : discount factor, d[k] = d(0,k)
// f : forward rate, f[k] = f(k-1,k) 
// g(a,r,pv1) : pv2 - pv1
// pv1 : present value in variable rate
// pv2 : present value in fixed rate
// r : fixed rate
// s : spot rate, s[k] = s(k)
// x : cash flow in variable rate, x[0] = x(k)
// y : cash flow in fixed rate, y = a * r

'use strict'

// function
const g  = (a, r, pv1) => { // g = pv2 - pv1
    let d=[];
    d[1] = 1 / (1 + r) ** 1;
    d[2] = 1 / (1 + r) ** 2;
    d[3] = 1 / (1 + r) ** 3;
    d[4] = 1 / (1 + r) ** 4;
    d[5] = 1 / (1 + r) ** 5;
    d[6] = 1 / (1 + r) ** 6;
    const y = a * r;
    const pv2 = y * (d[1] + d[2] + d[3] + d[4] + d[5] + d[6]);
    return pv2 - pv1;
}
const sum = (x, y) => x + y;

// input
const a = 1000;
const s = [0.00, 0.070, 0.073, 0.077, 0.081, 0.084, 0.088];

// calculation
let   f = [0,    0,     0,     0,     0,     0,     0];
for(let i = 0; i < s.length; i += 1){
    if(i == 0){
        f[0] = 0;
    }else if (i == 1){
        f[1] = s[1];
    }else {
        f[i] = (1 + s[i]) ** i / (1 + s[i - 1]) ** (i - 1) - 1;
    }
}
const x   = f.map((x)    => a * x);
const d   = s.map((_, i) => 1 / (1 + s[i]) ** i);
const pv1 = x.map((_, i) => x[i] * d[i]).reduce(sum, 0);
let r;
for(let i = 8700; i < 8900; i += 1){
    r = i / 1e5;
    if( g(a, r, pv1) > 0){
        break;
    }
}

// output
console.log('10.11.js');
console.log('a', a);
console.log('s', ...s.map(x => x.toFixed(3).padStart(7)));
console.log('f', ...f.map(x => x.toFixed(3).padStart(7)));
console.log('x', ...x.map(x => x.toFixed(3).padStart(7)));
console.log('d', ...d.map(x => x.toFixed(3).padStart(7)));
console.log('pv1 in variable rates ', pv1);
console.log('constant r, g(r)', r, g(a,r,pv1));
// end