Savings Growth Calculator

The first term, P₀(1 + r/n)ⁿᵗ, is the future value of the lump sum growing entirely on its own, and the second term, PMT × [((1 + r/n)ⁿᵗ − 1) / (r/n)], is the future value of the recurring deposits growing as an annuity. Both terms compound at the identical periodic rate; they are simply added together because the lump sum and the deposit stream are two separate pools of money that happen to share one interest rate.

Set either input to zero and its term drops out cleanly. The formula does not need a special case for a missing lump sum or missing deposits.

Depositing more often produces a higher final balance at the same annual rate, because money reaches the account sooner and has more periods left to compound. Switching $150 a month to $450 a quarter deposits the same annual amount, but the monthly version gets each dollar working roughly six weeks earlier on average.

The effect is real but usually modest next to the size of the rate itself. Raising the rate by a percentage point typically moves the final balance far more than switching monthly deposits to quarterly ones.

This calculator assumes an ordinary annuity, meaning each deposit is credited at the end of its period, so the very last deposit earns no interest at all. A deposit made at the start of the period instead, an annuity due, would sit through one extra period of compounding, making every deposit worth very slightly more.

The difference between the two conventions is exactly one period of interest on the deposit amount, which is a small effect over many periods but not zero, so it is worth knowing which assumption a calculator is making before comparing results across tools.

With zero initial savings the lump-sum term vanishes and the formula becomes a pure annuity: FV = PMT × [((1 + r/n)ⁿᵗ − 1) / (r/n)]. Every dollar in the final balance then comes from either a deposit or the interest earned on prior deposits.

This is the common case for someone starting a savings goal from scratch rather than seeding it with existing funds. The calculator handles it automatically without any extra input.

Not directly, this calculator assumes a single fixed deposit amount for every period across the entire timeframe. If contributions are expected to rise, for example with an annual raise, the closest workaround is to run the calculator separately for each stretch of years at its own deposit amount, using the prior stretch's final balance as the next stretch's initial savings.

A dedicated growing-annuity formula exists for this case, but it adds a second rate variable and falls outside the scope of a fixed-deposit tool like this one.

Enter the annual rate actually paid or credited on the account, the stated annual percentage rate for savings and money-market accounts, or an expected average annual return for investment-based savings. The calculator then divides that rate by the number of periods per year to get the periodic rate used in every compounding step.

Because future returns on anything other than a fixed-rate savings account are estimates, treat any result beyond the next year or two as an illustration of the mathematics rather than a guarantee.

A plain compound interest calculation grows a single lump sum with no further deposits, while this calculator adds a recurring deposit stream on top of that lump sum. Set the recurring deposit to zero here and the two calculators produce identical results, since the annuity term disappears entirely.

The dedicated compound interest calculator is the simpler tool when there is no ongoing contribution to model.