C++，利息计算器不显示正确的输出

Question

问题是“编写一个程序，读取初始投资余额和利率，然后打印投资达到 100 万美元所需的年数。”

• 我输入的金额是 100，利率是 3。但是当我编译并运行时，输出是 29，这是不正确的，因为数量只有 187，根本不接近一百万。

/*
Question: Write a program that reads an initial
investment balance and an interest rate, then 
prints the number of years it takes for the 
investment to reach one million dollars.
*/

#include <iostream>

using namespace std;

int main()
{
    //Obtain user amount
    double amount;
    cout << "Please enter an initial investment balance ($0.00): $";
    cin >> amount;

    //Obtain user interest rate
    double interest_rate;
    cout << "Please enter an interest rate: ";
    cin >> interest_rate;

    //Convert interest rate to decimal
    interest_rate = interest_rate / 100;
    int time = 1;

    //Calculate how many years
    while (amount < 1000000)
    {
        amount = amount * (1 + (interest_rate * time));
        ++time;
    }
    
    //Display years
    cout << "Years to reach one million: " << time;
    return 0;
}

我期望的输出是:

“达到一百万年:333300”

因为 333300 正好是一百万。

Answer 1

一年后，金额会增长到

amount * (1 + interest_rate)

两年后，数量增长到

amount * (1 + interest_rate) * (1 + interest_rate)

假设您的利率每年复利。您包含的 time 和连续乘以 amount 是错误的。

请注意，这里有一个封闭形式的解决方案。对于利率r，初始金额I，最终金额A，年数t是

t = ln(A / I) / ln(1 + r)

您需要对其进行汇总。