Solve for the lowest modeled annual rate
Use this tool when the target, initial balance, duration, recurring deposit, deposit frequency, compounding frequency, and deposit timing are known. Frequencies can be annual, semiannual, quarterly, monthly, weekly, or daily. The additional deposit is the amount per selected deposit interval.
Search and cash-flow assumptions
This is a product-defined numerical scenario. Years times compounding frequency is rounded to a whole number of periods. Deposits are redistributed into equal cash flows per compounding period. For each period, a beginning deposit is added before growth or an end deposit after growth. The rate search starts with a 100% annual upper bound and doubles it while that bound remains below 10,000%; if the doubling step reaches or exceeds 10,000%, the target is reported as unsupported. If deposits alone reach the goal, the answer is 0%.
For a $50,000 goal, $10,000 initial balance, five years, $500 monthly deposits, annual compounding, and end-of-period timing, deposits total $40,000 and the lowest modeled annual rate is 8.08%. Moving the deposits to the beginning of each annual period lowers the result to 6.45% in this model. With monthly compounding and end timing, it is 7.02%. Compare timing and compounding cases only after confirming that the deposit conversion describes the intended cash flow.
Checklist before interpreting the rate
Verify the deposit amount is per selected frequency, beginning/end timing is correct, and all money uses one currency. Then compare the result with an actual account’s stated rate, compounding convention, fees, and deposit rules rather than treating it as an available offer.
Goal, balance, deposits, and years must be valid nonnegative values, with years at least 0.01. Unknown frequencies or timing, blanks, and invalid numeric inputs are invalid. A goal already met returns 0%; a target outside the supported search has no result.
The displayed total deposited uses the unrounded years × deposits per year calculation, while the modeled cash flows use the rounded number of compounding periods. For fractional years, those two period counts can diverge.
This excludes taxes, fees, variable rates, withdrawals, inflation, and regulatory APY disclosures. It is not investment advice or a promised yield. For a fixed monthly-rate projection, use the savings calculator.