Explanation
Savings with regular deposits
Regular deposits often matter more than the starting balance. This estimate adds each deposit at the end of the month, after that month’s interest.
Choose the question and enter values
Enter the current balance, the same deposit for every month, a nominal annual interest rate, and the number of months. The rate is divided by twelve; an effective annual yield is a different convention.
Balance = Pqⁿ + D(1 + q + … + qⁿ⁻¹), where q = 1 + R/1200.
| P | Starting balance (USD) |
|---|---|
| D | Monthly deposit (USD) |
| R | Interest rate |
| n | Saving period |
A year of deposits without interest
| Starting balance | 1,000 |
|---|---|
| Monthly deposit | 100 |
| Interest rate | 0 |
| Saving period | 12 |
| Result | $2,200 |
Start with $1,000 and repeat balance × (1 + 0/1200) + $100 for 12 months. Starting balance plus deposits = $2,200; the final balance rounded once to cents = $2,200.
1 month: $100 at 12% plus a $10 deposit
| Starting balance | 100 |
|---|---|
| Monthly deposit | 10 |
| Interest rate | 12 |
| Saving period | 1 |
| Result | $111 |
Start with $100 and repeat balance × (1 + 12/1200) + $10 for 1 months. Starting balance plus deposits = $110; the final balance rounded once to cents = $111.
2 months: $100 at 12% plus $10 deposits
| Starting balance | 100 |
|---|---|
| Monthly deposit | 10 |
| Interest rate | 12 |
| Saving period | 2 |
| Result | $122.11 |
Start with $100 and repeat balance × (1 + 12/1200) + $10 for 2 months. Starting balance plus deposits = $120; the final balance rounded once to cents = $122.11.
Diagram of this result
A bar splits the final balance into the starting balance, the deposits you made and the interest earned, all from the same projection.
The three parts and the final balance are listed as exact dollar amounts beside the bar.
Common mistakes
Do not enter an effective annual yield as a nominal rate without converting it. Beginning-of-month deposits would earn an extra month of interest.
Assumptions and limits
USD only. Constant interest and end-of-month deposits; no withdrawals, fees or taxes. Interest is retained at high precision and the final balance is rounded once, so an account that settles interest monthly can differ. Educational estimates only, not financial, tax or investment advice.
Are deposits included in the result?
Yes. The balance includes the starting money, every monthly deposit, and projected interest.
Method and references
The balance follows from monthly compounding and the finite geometric series. Investor.gov explains compound interest and saving assumptions at https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator . The examples above are independent fixtures for this method.