Finance formula
How to calculate monthly savings needed
This formula estimates the monthly deposit needed to reach a target balance by a deadline.
Direct answer
Formula
PMT = (FV - PV(1 + r)^n) / (((1 + r)^n - 1) / r)
Use the table below to match each symbol with the right input. Keep units consistent before you start.
Monthly savings needed formula
Start here when you only need the equation and variable names.
Formula
PMT = (FV - PV(1 + r)^n) / (((1 + r)^n - 1) / r)
This formula estimates the monthly deposit needed to reach a target balance by a deadline.
Variable meanings
Check each symbol, meaning, and unit before you calculate.
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PMT | Monthly contribution | Deposit needed each month. | currency per month |
| FV | Future goal | Target balance. | currency |
| PV | Current savings | Amount already saved. | currency |
| r | Monthly rate | Annual return divided by 12. | Depends on inputs |
| n | Months | Number of monthly deposits. | months |
When to use this formula
Check that your situation matches the formula before you trust the result.
- Helpful for emergency funds, down payments, tuition goals, and other fixed savings targets.
Step-by-step method
Follow these steps when you are solving it by hand.
- 1Convert the annual return to a monthly decimal rate.
- 2Convert the timeline to months.
- 3Grow current savings to the goal date.
- 4Divide the remaining goal by the deposit growth factor.
Examples
These sample numbers show the order of operations and units.
Two-year goal
FV
$10,000
PV
$1,000
r
0.04 / 12
n
24
- 1.PMT = (10000 - 1000(1.003333)^24) / (((1.003333)^24 - 1) / 0.003333)
- 2.PMT = 357.49
Result
You need to save about $357.49 per month.
Five-year goal
FV
$25,000
PV
$5,000
r
0.03 / 12
n
60
- 1.PMT = (25000 - 5000(1.0025)^60) / (((1.0025)^60 - 1) / 0.0025)
- 2.PMT = 296.87
Result
You need to save about $296.87 per month.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
- Using an annual rate where the monthly savings needed formula needs a monthly or period rate.
- Entering 8 instead of 0.08 when the formula calls for a decimal rate.
- Comparing results across different time periods without converting them first.
- Rounding each step instead of rounding the final answer.
Open the Savings Goal Calculator
Open the calculator for the answer without rewriting the formula.
Enter your values in the related calculator, then compare the output with the hand method above.
Open Savings Goal CalculatorFAQs
Short answers for common formula questions.
Can I calculate Monthly savings needed by hand?
Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.
Why does my Monthly savings needed result differ from another calculator?
Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.
When is the Savings Goal Calculator better than hand math?
Open the Savings Goal Calculator to check several scenarios or skip the hand arithmetic.