計算不同複利期和計息期的年金

誰能幫我解決這個問題？

2010 年 7 月，邁克每半年將 100 美元存入一個賬戶，每季度複利一次，名義年利率為 7%，為期三年。2013 年 7 月，他將存款增加到每 6 個月 200 美元，但當年的利率降至 5%。2014 年 7 月，他以 6% 的固定利率在銀行再存入 2000 美元（除了之前的存款），為期 5 年。2014 年 7 月至 2018 年底的利率保持在 6%。找出他在 2018 年底儲蓄的價值。

感謝@D Stanley 的提示

+------------------+-----------+--------------+--------------+---------+---------------------+
|                  |deposits   |principals**  |interest rate |interest*|accumulated interest |
+------------------+-----------+--------------+--------------+---------+---------------------+
|2nd half 2010     |100        |100           |0.07          |3.53     |3.53                 |
|1st half 2011     |200        |203.53        |0.07          |7.19     |10.72                |
|2nd half 2011     |300        |310.72        |0.07          |10.97    |21.69                |
|1st half 2012     |400        |421.69        |0.07          |14.89    |36.57                |
|2nd half 2012     |500        |536.57        |0.07          |18.94    |55.52                |
|1st half 2013     |600        |655.52        |0.07          |23.14    |78.66                |
|2nd half 2013     |800        |878.66        |0.05          |22.10    |100.77               |
|1st half 2014     |1000       |1100.77       |0.05          |27.69    |128.46               |
|2nd half 2014     |3200       |3328.46       |0.06          |100.60   |229.06               |
|1st half 2015     |3400       |3629.06       |0.06          |109.69   |338.75               |
|2nd half 2015     |3600       |3938.75       |0.06          |119.05   |457.80               |
|1st half 2016     |3800       |4257.80       |0.06          |128.69   |586.49               |
|2nd half 2016     |4000       |4586.49       |0.06          |138.63   |725.12               |
|1st half 2017     |4200       |4925.12       |0.06          |148.86   |873.98               |
|2nd half 2017     |4400       |5273.98       |0.06          |159.41   |1033.38              |
|1st half 2018     |4600       |5633.38       |0.06          |170.27   |1203.65              |
|2nd half 2018     |4800       |6003.65       |0.06          |181.46   |1385.11              |
+------------------+-----------+--------------+--------------+---------+---------------------+

*計算利息列的公式為

interest = (principal * (1 + (interest rate / 4) ) ^ (0.5 * 4) ) - principal
0.5 is a half of a year
4 is the number of compounding periods

** 本金為期初存款+累計利息

根據我的計算，他應該在 2018 年底之前在他的帳戶中有6185.11

• 6185.11 = 4800 + 1385.11
• 6185.11 = 6003.65 + 181.46

使用複利存款最終價值的公式

i = 0.07
d = 100
n = 6

r = (1 + i/4)^2 - 1 = 0.0353063
a1 = (d (1 + r) ((1 + r)^n - 1))/r = 678.663

i = 0.05
d = 200
n = 2

r = (1 + i/4)^2 - 1 = 0.0251562
a2 = (d (1 + r) ((1 + r)^n - 1))/r + a1 (1 + r)^n = 1128.46

i = 0.06
d = 200
x = 2000
n = 9

r = (1 + i/4)^2 - 1 = 0.030225
a3 = (d (1 + r) ((1 + r)^n - 1))/r + (a2 + x) (1 + r)^n = 6185.11

2018 年底的儲蓄價值為 6185.11 美元

引用自：https://money.stackexchange.com/questions/113081