# Savings goal calculator

> Calculate how much to save each month to reach a savings goal by a date, or how long a monthly deposit takes to get there, with interest.

交互版本：https://www.calcopenly.com/zh/finance/savings-goal-calculator
主题：财务计算器

The monthly deposit needed is what closes the gap between the goal and what your current savings will grow to: C = (G − S(1 + i)^n) ÷ (((1 + i)^n − 1) ÷ i), where G is the goal, S the amount already saved, i the monthly rate and n the number of months. In the other mode, the number of months comes from logarithms of the same equation and is rounded up to the month in which the goal is reached.

With the defaults, reaching 50,000 in 5 years from 5,000 already saved at 4% a year takes 662.08 a month. The 60 deposits add up to 39,724.61, and interest supplies the remaining 5,275.39 on top of the 5,000 you started with.

Interest is compounded monthly at a fixed rate, with deposits at the end of each month unless you choose the start under More options. Tax on interest and changes in the rate are not included.

## 输入

- **我要计算** (选项：Monthly deposit needed, Time to reach the goal)
- **储蓄目标**
- **Already saved**
- **Monthly deposit**
- **Time to goal**
- **Interest rate (per year)**: Compounded monthly
- **Deposits made at** (选项：End of month, Start of month)

## 结果

- Monthly deposit needed — 主要结果
- Months to reach the goal
- Time to goal
- Monthly deposits in total
- Interest earned
- Balance at the end

## 公式

$$
C = \frac{G - S(1+i)^{n}}{\frac{(1+i)^{n}-1}{i}},\qquad n = \frac{\ln\!\left(\frac{G + C/i}{S + C/i}\right)}{\ln(1+i)},\quad i = \frac{r}{12}
$$

## 计算示例

### 50,000 in 5 years from 5,000 at 4%

- 我要计算: Monthly deposit needed
- 储蓄目标: 50,000
- Already saved: 5000
- Time to goal: 5 years
- Interest rate (per year): 4%
- Deposits made at: End of month
- **Monthly deposit needed: 662.08**
- 核验来源：Python decimal: (50000 − 5000·(1+0.04/12)^60) / (((1+i)^60 − 1)/i) = 662.0768…; same as Excel =PMT(4%/12,60,-5000,50000)

### Deposits at the start of each month

- 我要计算: Monthly deposit needed
- 储蓄目标: 50,000
- Already saved: 5000
- Time to goal: 5 years
- Interest rate (per year): 4%
- Deposits made at: Start of month
- **Monthly deposit needed: 659.88**
- 核验来源：Python decimal, annuity-due factor: 659.8772…

### Zero rate

- 我要计算: Monthly deposit needed
- 储蓄目标: 12,000
- Already saved: 0
- Time to goal: 1 year
- Interest rate (per year): 0%
- **Monthly deposit needed: 1,000.00**
- **Interest earned: 0.00**
- 核验来源：12000 / 12 by definition

### Already saved more than the goal

- 我要计算: Monthly deposit needed
- 储蓄目标: 1000
- Already saved: 2000
- Time to goal: 5 years
- Interest rate (per year): 4%
- **Monthly deposit needed: 0.00**
- 核验来源：Starting balance exceeds the goal, so no deposit is needed

### Time to 50,000 saving 500 a month at 4%

- 我要计算: Time to reach the goal
- 储蓄目标: 50,000
- Already saved: 5000
- Monthly deposit: 500
- Interest rate (per year): 4%
- Deposits made at: End of month
- **Months to reach the goal: 77**
- **Balance at the end: 50,269.70**
- **Time to goal: 6 years 5 months**
- 核验来源：Python decimal month-by-month simulation (first month with balance ≥ goal is 77; closed form n* = 76.595)

### Time at zero rate

- 我要计算: Time to reach the goal
- 储蓄目标: 10,000
- Already saved: 1000
- Monthly deposit: 300
- Interest rate (per year): 0%
- **Months to reach the goal: 30**
- **Interest earned: 0.00**
- 核验来源：(10000 − 1000) / 300 = 30 months exactly

## 常见问题

### How much do I need to save each month to reach a goal?

Subtract what your current savings will grow to from the goal, then divide by the annuity factor ((1 + i)^n − 1) ÷ i. To reach 50,000 in 5 years from 5,000 at 4% compounded monthly, you need 662.08 a month; Excel's =PMT(4%/12, 60, -5000, 50000) gives the same. With no interest the same goal takes (50,000 − 5,000) ÷ 60 = 750 a month.

### How long will it take to reach my savings goal?

Solve the savings equation for the number of months and round up. Starting from 5,000 and saving 500 a month at 4%, the balance first passes 50,000 in month 77, after 6 years 5 months; raising the deposit to 750 cuts that to 54 months. Excel's NPER function solves the same equation.

### How much does interest help a savings goal?

More the longer the horizon. Over 5 years, 4% interest cuts the deposit needed for 50,000 from 750 to 662.08 a month, and 5% cuts it to 640.87. Over 10 years at 4%, the deposit falls to 288.94 a month and interest supplies 10,327.63 of the 50,000.

### Does it matter if I save at the start or end of the month?

Slightly: a deposit made at the start of the month earns one extra month of interest. For 50,000 in 5 years from 5,000 at 4%, the deposit needed is 659.88 at the start of each month against 662.08 at the end, a difference of 2.20 a month.

### “Savings goal calculator”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：6。 例如，“50,000 in 5 years from 5,000 at 4%”根据Python decimal: (50000 − 5000·(1+0.04/12)^60) / (((1+i)^60 − 1)/i) = 662.0768…; same as Excel =PMT(4%/12,60,-5000,50000)进行核验。

### 这种方法出自哪里？

Microsoft Excel PMT function; Microsoft Excel NPER function.

## 来源

- [Microsoft Excel PMT function](https://support.microsoft.com/office/pmt-function-0214da64-9a63-4996-bc20-214433fa6441)
- Microsoft Excel NPER function

_仅用于规划。贷款机构、税务机关和市场采用各自的舍入方式、费用和规则；作出承诺前，请向相关机构确认数值。_