# 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.

इंटरैक्टिव संस्करण: https://www.calcopenly.com/hi/finance/savings-goal-calculator
विषय: वित्त कैलकुलेटर

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.

## इनपुट

- **मैं निकालना चाहता हूँ** (विकल्प: Monthly deposit needed, Time to reach the goal)
- **बचत लक्ष्य**
- **Already saved**
- **Monthly deposit**
- **Time to goal**
- **Interest rate (per year)**: Compounded monthly
- **Deposits made at** (विकल्प: End of month, Start of month)

## नतीजे

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

## सूत्र

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

## हल किए गए उदाहरण

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

- मैं निकालना चाहता हूँ: Monthly deposit needed
- बचत लक्ष्य: 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**
- जाँच का स्रोत: 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

- मैं निकालना चाहता हूँ: Monthly deposit needed
- बचत लक्ष्य: 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**
- जाँच का स्रोत: Python decimal, annuity-due factor: 659.8772…

### Zero rate

- मैं निकालना चाहता हूँ: Monthly deposit needed
- बचत लक्ष्य: 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**
- जाँच का स्रोत: 12000 / 12 by definition

### Already saved more than the goal

- मैं निकालना चाहता हूँ: Monthly deposit needed
- बचत लक्ष्य: 1000
- Already saved: 2000
- Time to goal: 5 years
- Interest rate (per year): 4%
- **Monthly deposit needed: 0.00**
- जाँच का स्रोत: Starting balance exceeds the goal, so no deposit is needed

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

- मैं निकालना चाहता हूँ: Time to reach the goal
- बचत लक्ष्य: 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**
- जाँच का स्रोत: Python decimal month-by-month simulation (first month with balance ≥ goal is 77; closed form n* = 76.595)

### Time at zero rate

- मैं निकालना चाहता हूँ: Time to reach the goal
- बचत लक्ष्य: 10,000
- Already saved: 1000
- Monthly deposit: 300
- Interest rate (per year): 0%
- **Months to reach the goal: 30**
- **Interest earned: 0.00**
- जाँच का स्रोत: (10000 − 1000) / 300 = 30 months exactly

## सवाल

### 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” कितना सटीक है?

सटीकता आपके इनपुट और विधि की मान्यताओं पर निर्भर करती है। दशमलव गणना 50 सार्थक अंकों का उपयोग करती है, लेकिन अनुमान, संख्यात्मक विधियाँ और स्रोत डेटा कम सटीक हो सकते हैं। दिखाए गए मानों को पूर्णांकित करने से ये सीमाएँ दूर नहीं होतीं। स्वतंत्र स्रोतों के हल किए गए उदाहरणों से जाँच: 6। उदाहरण के लिए, “50,000 in 5 years from 5,000 at 4%” की जाँच 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) से की गई है।

### इस विधि का स्रोत क्या है?

Microsoft Excel PMT function; Microsoft Excel NPER function.

## स्रोत

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

_केवल योजना बनाने के लिए। ऋणदाता, कर अधिकारी और बाज़ार अपने पूर्णांकन, शुल्क और नियम लागू करते हैं; कोई प्रतिबद्धता करने से पहले उनसे आँकड़ों की पुष्टि करें।_