复利计算器没有产生正确的值

Question

我正在创建一个在 javascript 中每月贡献的复利公式，用于填充 chartkick.js 图表，以显示每年年底本金增长到的总金额。这是我遵循的公式。

Compound Interest For Principal
P(1 + r/n) ^ nt
Future Value of a Series
PMT * (((1 + r/n)^nt - 1) / (r/n)) * (1+r/n) 

A = [Compound Interest for Principal] + [Future Value of a Series]

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
PMT = the monthly payment
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year AND additional payment frequency
t = the number of years the money is invested or borrowed for 
*/

这是我的 javascript：

P = $("#start-amount").val().replace(/[^\d\.]/g, '');
var t = $("#years").val(); 
var PMT = $("#contributions-amount").val().replace(/[^\d\.]/g, '');  
var n = $("#contribution-rate").val();
//If you choose monthly it is equal to 12 and annually it is equal to 1 
//Convert Interest Rate to Decimal
var r_percentage = $("#interest-rate").val().replace(/[^\d\.]/g, '');
var r = parseFloat(r_percentage) /  100.0;

//Create an arary with list of numbers less than number of years
var t_arr = [];
for (i = 0; i <= t; i++) {
    if (i > 0 && i <= t) {
        t_arr.push(i)
    }
}

//For Chartkick Chart
data = [
{"name": "With interest", "data": {}
},
{"name": "No Interest", "data": {}
}];

/* 
Needs to be like this!
data = [
  {"name":"Workout", "data": {"2013-02-10 00:00:00 -0800": 3, "2013-02-17 00:00:00 -0800": 4}},
  {"name":"Call parents", "data": {"2013-02-10 00:00:00 -0800": 5, "2013-02-17 00:00:00 -0800": 3}}
];*/

/*With Interest
J is equal to each individual year less than the total number of years*/
for (j = 1; j <= t_arr.length; j++) {
    var compound_interest_for_principal = P * (Math.pow(1 + r / n, n * t));
    var value_rounded1 = Math.round(compound_interest_for_principal * 100) /100;
    var future_value_of_series = PMT * (Math.pow(1 + r / n, n * j) - 1) / (r / n) * (1 + r / n);
    var value_rounded2 = Math.round(future_value_of_series * 100) / 100;
    var A = value_rounded1 + value_rounded2;
    var A = A.toFixed(2);
    if (data[0]["data"][j] === undefined) {
        data[0]["data"][j] = A;
    }
}

/*Without Interest */
for (k = 1; k <= t_arr.length; k++) {
    var r = 0;
    var principal_no_interest= P;
    var value_rounded1 = Math.round(principal_no_interest * 100) /100;
    var monthly_no_interest = PMT * n * k;
    var value_rounded2 = Math.round(monthly_no_interest * 100) / 100;
    var A = value_rounded1 + value_rounded2;
    var A = A.toFixed(2);
    if (data[1]["data"][k] === undefined) {
        data[1]["data"][k] = A;
    }
}
new Chartkick.LineChart("savings-chart", data, {"discrete": true});

我正在测试的值是 P = 1,000 美元，r = 5%（年利率），PMT = 每月 100 美元，n = 12（每年复利的次数和额外的付款频率）。

问题出在我得到的值。

1 年的利息后，我得到 2,880 美元，我应该得到 2,277 美元。 10 年后，我应该得到 17,065.21 美元，但我得到了 17,239.94 美元。我不明白为什么它在原版的基础上增加了大约 1,800 美元，而应该增加了大约 1,200 美元。有什么建议吗？

Answer 1

你可以检查一下

var result = PMT * (Math.pow(1 + r / n, nt) - 1) / (r / n) * (1 + r / n);

Answer 2

感谢大家的帮助。我找到了解决方案。这是错误代码与正确代码的对比：

/*
Formula to Implement
P(1 + r/n) ^ nt
Future Value of a Series
PMT * (((1 + r/n)^nt - 1) / (r/n)) * (1+r/n) 

A = [Compound Interest for Principal] + [Future Value of a Series]

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
PMT = the monthly payment
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year AND additional payment frequency
t = the number of years the money is invested or borrowed for 
/*

/*INCORRECT SOLUTION
J is equal to each individual year less than the total number of years*/
for (j = 1; j <= t_arr.length; j++) {
    //Correct
    var compound_interest_for_principal = P * (Math.pow(1 + r / n, n * t));
    //Correct
    var a= Math.round(compound_interest_for_principal * 100) /100;
    //Incorrect
    var future_value_of_series = PMT * (Math.pow(1 + r / n, n * j) - 1) / (r / n) * (1 + r / n);
    var b = Math.round(future_value_of_series * 100) / 100;
    var A = a + b;
    var A = A.toFixed(2);
    if (data[0]["data"][j] === undefined) {
        data[0]["data"][j] = A;
    }
}

//CORRECT SOLUTION
for (j = 1; j <= t_arr.length; j++) {
    //Incorrect
    var compound_interest_for_principal = P * (Math.pow(1 + r / n, n * j));
    var a = Math.round(compound_interest_for_principal * 100) / 100;
    var future_value_of_series = ((PMT * n) / r) * (Math.pow(1 + r / n, n * j) - 1) 
    var b = Math.round(future_value_of_series * 100) / 100;
    var A = a + b
    var A = A.toFixed(2);
    if (data[0]["data"][j] === undefined) {
        data[0]["data"][j] = A;
}