# 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.

직접 계산할 수 있는 페이지: https://www.calcopenly.com/ko/finance/savings-goal-calculator
분야: 금융 계산기

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.

## 입력

- **계산할 항목** (선택 항목: Monthly deposit needed, Time to reach the goal)
- **저축 목표**
- **Already saved**
- **Monthly deposit**
- **Time to goal**
- **Interest rate (per year)**: Compounded monthly
- **Deposits made at** (선택 항목: End of month, Start of month)

## 결과

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

## 공식

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

## 계산 예제

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

- 계산할 항목: Monthly deposit needed
- 저축 목표: 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**
- 검증 출처: 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

- 계산할 항목: Monthly deposit needed
- 저축 목표: 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**
- 검증 출처: Python decimal, annuity-due factor: 659.8772…

### Zero rate

- 계산할 항목: Monthly deposit needed
- 저축 목표: 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**
- 검증 출처: 12000 / 12 by definition

### Already saved more than the goal

- 계산할 항목: Monthly deposit needed
- 저축 목표: 1000
- Already saved: 2000
- Time to goal: 5 years
- Interest rate (per year): 4%
- **Monthly deposit needed: 0.00**
- 검증 출처: Starting balance exceeds the goal, so no deposit is needed

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

- 계산할 항목: Time to reach the goal
- 저축 목표: 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**
- 검증 출처: Python decimal month-by-month simulation (first month with balance ≥ goal is 77; closed form n* = 76.595)

### Time at zero rate

- 계산할 항목: Time to reach the goal
- 저축 목표: 10,000
- Already saved: 1000
- Monthly deposit: 300
- Interest rate (per year): 0%
- **Months to reach the goal: 30**
- **Interest earned: 0.00**
- 검증 출처: (10000 − 1000) / 300 = 30 months exactly

## 자주 묻는 질문

### 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”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 6. 예를 들어 “50,000 in 5 years from 5,000 at 4%”은 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)와 대조해 확인합니다.

### 이 계산 방법의 출처는 무엇인가요?

Microsoft Excel PMT function; Microsoft Excel NPER function.

## 출처

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

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