Compound Interest Formula
也称为: Future Value Formula, Compound Growth Formula
A = P \left(1 + \frac{r}{n}\right)^{nt}
A = P(1 + r/n)^(nt)它计算什么
Calculates the future value of an investment or loan with compound interest — where interest earns interest on itself over time.
变量
| 象征 | 姓名 | 描述 |
|---|---|---|
| A | Future Value | The amount of money accumulated after n years, including interest |
| P | Principal | The initial amount of money invested or borrowed |
| r | Annual Interest Rate | The annual interest rate as a decimal (e.g., 5% = 0.05) |
| n | Compounding Frequency | Number of times interest is compounded per year |
| t | Time | The number of years the money is invested or borrowed |
推导
Starting from simple interest for one period: after one compounding period, the balance is P(1 + r/n). After two periods, it becomes P(1 + r/n)². Generalizing to nt total periods gives the formula.
工作示例
1
r/n = 0.05/12 = 0.0041672
nt = 12 × 10 = 1203
(1 + 0.004167)^120 = 1.64704
A = 10000 × 1.6470 = $16,470.09结果: $16,470.09
常见错误
Don't forget to convert the percentage rate to a decimal
Make sure n and t use consistent units (both yearly)
This formula assumes no additional deposits — use the annuity formula for regular contributions
尝试计算器
相关公式
#interest#investment#savings#growth#time value of money