# 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.

Интерактивная версия: https://www.calcopenly.com/ru/finance/savings-goal-calculator
Тема: Финансовые калькуляторы

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.

## Входные данные

- **Что нужно найти** (варианты: Monthly deposit needed, Time to reach the goal)
- **Цель накоплений**
- **Already saved**
- **Monthly deposit**
- **Time to goal**
- **Interest rate (per year)**: Compounded monthly
- **Deposits made at** (варианты: End of month, Start of month)

## Результаты

- Monthly deposit needed — основной результат
- Months to reach the goal
- Time to goal
- Monthly deposits in total
- Interest earned
- Balance at the end

## Формула

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

## Примеры с решением

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

- Что нужно найти: Monthly deposit needed
- Цель накоплений: 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**
- Источник проверки: 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

- Что нужно найти: Monthly deposit needed
- Цель накоплений: 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**
- Источник проверки: Python decimal, annuity-due factor: 659.8772…

### Zero rate

- Что нужно найти: Monthly deposit needed
- Цель накоплений: 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**
- Источник проверки: 12000 / 12 by definition

### Already saved more than the goal

- Что нужно найти: Monthly deposit needed
- Цель накоплений: 1000
- Already saved: 2000
- Time to goal: 5 years
- Interest rate (per year): 4%
- **Monthly deposit needed: 0.00**
- Источник проверки: Starting balance exceeds the goal, so no deposit is needed

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

- Что нужно найти: Time to reach the goal
- Цель накоплений: 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**
- Источник проверки: Python decimal month-by-month simulation (first month with balance ≥ goal is 77; closed form n* = 76.595)

### Time at zero rate

- Что нужно найти: Time to reach the goal
- Цель накоплений: 10,000
- Already saved: 1000
- Monthly deposit: 300
- Interest rate (per year): 0%
- **Months to reach the goal: 30**
- **Interest earned: 0.00**
- Источник проверки: (10000 − 1000) / 300 = 30 months exactly

## Вопросы

### 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.

### Насколько точен «Savings goal calculator»?

Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 6. Например, «50,000 in 5 years from 5,000 at 4%» проверяется по источнику 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).

### Откуда взята методика?

Microsoft Excel PMT function; Microsoft Excel NPER function.

## Источники

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

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