An account balance mixes investment growth with money you added. Dividing the gain by total contributions does not account for how long each contribution was invested.
What this calculator supports
Caspenda estimates a money-weighted return for one initial investment followed by the same contribution at the end of every month. Enter the starting balance, monthly amount, whole years and final value. It does not accept irregular cash-flow dates, skipped contributions, withdrawals or XIRR. A dated cash-flow model is needed for those cases.
Three terms with different meanings
- Effective annualized return compounds the solved monthly rate over twelve months: (1 + i)12 − 1. This is the main result.
- Nominal annual rate is the rate quoted for a specified compounding frequency. With monthly compounding, it is 12 × i. It is shown separately so it can be compared with the input rate used by the Compound Interest Calculator.
- Real return means inflation-adjusted return. Using an effective nominal annual return, real return = (1 + annual return) ÷ (1 + inflation) − 1. This calculator does not make that adjustment.
A worked example you can reproduce
Start with $10,000, add $500 per month for 10 years, and end with $150,000. Contributions total $70,000 and investment growth is $80,000.
The monthly rate is approximately 1.01631%. The effective annualized return is about 12.9% (12.9011% before rounding). The equivalent nominal annual rate with monthly compounding is about 12.2% (12.1957% before rounding). Both describe the same monthly rate; neither is an inflation-adjusted return.
How the reverse calculation works
The engine solves FV = P × (1+i)N + M × ((1+i)N − 1) ÷ i for the monthly rate i. P is the starting balance, M is the fixed month-end contribution, and N is the number of months. When i is zero, FV = P + M × N.
The formula gives an equivalent constant rate, not a reconstruction of market prices. Its yearly breakdown is a modeled path, not your actual historical account balances.
Reading different outcomes
With no starting balance and $500 added monthly for ten years:
| Final balance | Effective annualized return | Nominal annual rate, monthly compounding |
|---|---|---|
| $86,542 | About 7.23% | About 7.00% |
| $60,000 | 0% | 0% |
| $50,000 | About −3.73% | About −3.79% |
Returns from a benchmark must cover the same dates and use a compatible contribution schedule and return convention. This estimate alone cannot show whether your timing or investment selection outperformed a market index.
Open the Investment Return Calculator. For purchasing-power terminology, see Investor.gov — Real Return.