程序和计算器答案之间的 0.5 差异

Question

我用 C++ 编写了这个程序，作为家庭作业的一部分简单计算了银行的利率。答案有一点不正确，但我仍然不明白为什么，当我尝试输入更高的数字时，错误会越来越大…… 关于如何解决这个问题的说明被注释为程序的第一行。

我尝试将涉及的变量从 float 切换到 double，然后再切换到 long double，结果仍然是相同的答案...

谁能知道为什么？

// Homework 2 Task 1.cpp : Show bank balance after loan with user-input factors
//Try the code with 100 deposited sum, 5% interest and 3 months total time
//The answer will show 302.087 whereas the true answer should be 302.507

#include "stdafx.h"
#include <iostream>
using namespace std;

long double compoundVal(unsigned int, unsigned short int, unsigned short int);

void main()
{
    unsigned int DepSum;
    unsigned short int IntRate, NrMonths;
    cout << "Please enther the amount you expect to deposit each month: ";
    cin >> DepSum;
    cout << "\nThe amount of money that you will have in your account after 6 months with Inte-rest Rate of 5% will be: "<<compoundVal(DepSum, 5, 6); //Answering the first part of this task, where the user has to specify the Deposit Sum, and will receive the amount after 6 months with interest of 5%
    cout << "\n\nYou can also see the account balance with interest rate and number of months of your choice.\nPlease enter the Interest Rate of your choice: ";
    cin >> IntRate;
    cout << "\nNow enter the number of months you intend to have the account: ";
    cin >> NrMonths;
    cout << "\nThis will be your account balance: " << compoundVal(DepSum, IntRate, NrMonths) << endl;
}

long double compoundVal(unsigned int d, unsigned short int i, unsigned short int n){
    long double c = (1.0 + (i / 1200.0));   //Finding the monthly percentage, and because the user inputs the yearly interest in %, we need to remove the %(*0.01) and /12 for 12 months/year.
    return((1.0 + (n - 1)*c)*d*c);      //The math formula that will give us the results of the calculation. 
}

Answer 1

您使用的公式似乎有误 - 但我不确定您从哪里得到它或它实际代表什么。预期的答案是简单的周期性复利。也就是说，每个月你计算newbalance = balance * (1 + annualrate/12) + deposit)。在您需要的三个月内迭代 3 次得到预期答案 302.5069 美元，而不是您从公式中获得的较低值 302.0868 美元。

Answer 2

您使用的公式有误。

3个月末第一个月的存款价值：d.c^3
3个月末第二个月存款的价值：d.c^2
3个月末第三个月的存款价值：d.c

如果概括为N个月，则N个月末您的入金总额为：

d(c + c^2 + c^3 + ... + c^N)

该总和的值为：d.c.(c^N - 1)/(c-1)

如果您插入此公式，您将得到正确答案：302.507。

公式

sum = d(c + c^2 + c^3 + ... + c^N)

两边乘以c,

sum.c = d(c^2 + c^3 + c^4 + ... + c^(N+1))

两个方程相减，

sum(c-1) = d(c^(N+1) - c) = d.c(c^N - 1)
sum = d.c(c^N - 1)/(c-1)

程序和计算器答案之间的 0.5 差异

0.5 difference between program and calculator answer

c++

visual-c++