如果一个人投资了钱，然后每月投资该投资的月收入，那么总收入是多少

Question

假设我投资1000欧元，预计一年内收益+10%，因此为1100欧元。每个月的收入是91.667，我每个月都会再次投资，再加上91.667的10%，额外的利息。

以下算法正确吗？

totalMoney=1100;
moneyPerMonth=0;
for i=1:12
moneyPerMonth=(moneyPerMonth+totalMoney)/12
totalMoney=totalMoney+moneyPerMonth/12
end

我得到以下结果：

moneyPerMonth =  91.667
totalMoney =  1107.6
moneyPerMonth =  99.942
totalMoney =  1116.0
moneyPerMonth =  101.33
totalMoney =  1124.4
moneyPerMonth =  102.14
totalMoney =  1132.9
moneyPerMonth =  102.92
totalMoney =  1141.5
moneyPerMonth =  103.70
totalMoney =  1150.1
moneyPerMonth =  104.49
totalMoney =  1158.8
moneyPerMonth =  105.28
totalMoney =  1167.6
moneyPerMonth =  106.08
totalMoney =  1176.5
moneyPerMonth =  106.88
totalMoney =  1185.4
moneyPerMonth =  107.69
totalMoney =  1194.3
moneyPerMonth =  108.50
totalMoney =  1203.4

这意味着我发现我的收入从+10%增加到20034%，总收入为1203.4。

这是正确的吗？

Answer 1

有两件事：首先，你不清楚你关于复利的问题——如果10%的数字每年复利，那么到年底你确实会有1100，但你的月利率不会是0.1/12或0.008333。如果你用这个数字进行月度计算，你将按月复利，这将导致有效年利率为10.471%，而不是10%。要获得10%的有效年利率，您的月利率仅为0.007974。

一旦你决定要使用哪一个，剩下的就相当简单了。例如，使用python:

annual =  0.007974 #the code below uses this rate, but you can easily change it to "monthly"
monthly = 0.008333
months = 12
investment = 1000
balance = investment
print('after month',"taccrued int","tbalance",)
for m in range(months):    
interest = balance*annual
balance+=interest    
print(m+1, 'tt',format(interest,".2f"), 'tt',format(balance,".2f"))

输出：

after month accrued int balance
1        7.97        1007.97
2        8.04        1016.01
3        8.10        1024.11
4        8.17        1032.28
5        8.23        1040.51
6        8.30        1048.81
7        8.36        1057.17
8        8.43        1065.60
9        8.50        1074.10
10       8.56        1082.66
11       8.63        1091.30
12       8.70        1100.00