The savings between two prices in a savings plan is the difference between the future values produced by two different deposit levels, and the standard formula for projecting it combines a lump-sum growth term with a future-value-of-an-annuity term, giving you FV = initial × (1 + i)^N + contribution × ((1 + i)^N − 1) / i, where i is the periodic interest rate and N is the total number of periods. Apply it once for each deposit amount you want to compare, subtract the two future values, and the gap between them is the extra savings produced by contributing more. The same arithmetic also reveals how much of the final balance in either scenario is money you actually deposited versus interest the bank paid you, since contributions equal your starting balance plus every deposit, and interest earned equals the future value minus those contributions. This is the calculation a savings calculator runs in your browser whenever you adjust an input.
What the Savings Between Two Prices Means in a Savings Plan
The phrase "savings between two prices" usually points to a discount context, where you subtract a sale price from a sticker price to see what you kept. In a savings plan, the same idea works on a different axis: you pick two deposit levels, two interest rates, or two time horizons, run each through the future value formula, and subtract to see the gap. The "savings" is then the extra balance that the larger contribution (or the better rate, or the longer runway) produces at the end of the horizon. That number is what tells you whether doubling your monthly deposit is worth the discipline, or whether waiting two more years matters more than switching to a higher-yield account.
This framing matters because savings rarely grow from a single deposit in real life. Money lands in an account through paychecks, automatic transfers, or quarterly bonuses, and each contribution begins earning interest the moment it arrives. A model that treats savings as one big lump sum misses that stream. A model that treats savings as a recurring series of deposits — the approach used by the Savings Calculator — captures how an emergency fund, a vacation pot, or a down payment actually behaves over months and years.
The Two Formulas Behind the Number
Every projection of recurring savings rests on two standard pieces, both built on compound interest, which is the principle that each period's interest is added to the balance so the next period earns interest on interest as well as on the original principal.
First, your starting balance grows by compound interest on its own: initial × (1 + i)^N, where i is the periodic interest rate (annual rate divided by the number of compounding periods per year) and N is the total number of periods. After ten years of monthly compounding at 5%, a $1,000 starting balance grows to roughly $1,647 because the rate is applied 120 times rather than 10. The mechanics of this growth are described in detail on the Compound interest page.
Second, every deposit you add during the plan grows as an ordinary annuity, which is a series of equal payments made at the end of each compounding period: contribution × ((1 + i)^N − 1) / i. The ordinary-annuity convention assumes each deposit lands at the end of its period, which is the standard, slightly conservative assumption; depositing at the start of each period would earn a little more interest. The combined formula is the future value of a savings plan with a starting balance plus a stream of contributions, and it is the same calculation summarized on the Future value reference page.
Total contributions equal your starting balance plus every deposit you make, and interest earned equals the future value minus those contributions. That split is what lets you see, at a glance, how much of the final balance is money you set aside versus growth the account produced on its own.
How to Calculate Savings Between Two Deposit Scenarios
The cleanest way to compare two deposit levels is to run each one through the same model and subtract. The Savings Calculator does this in a single screen, updating the projection every time you change an input.
- Enter your starting balance in the first field. This is the amount already sitting in the account before any new deposits.
- Enter the amount you deposit each period — the recurring contribution you want to model for the first scenario.
- Pick how often you deposit: monthly, quarterly, or annually. This sets the number of compounding periods per year, which feeds the periodic rate i.
- Enter the annual interest rate as a percentage (for example, 5 for five percent) and the number of years you want to project.
- Read the future value along with total contributions and interest earned. The result updates in real time as you adjust any input.
- To compare scenarios, change the deposit amount to your second value (or change the rate or the years), read the new future value, and subtract the two numbers to see the savings gap.
For readers who want to see the math on paper before they trust the tool, a single worked example makes the formula concrete. Suppose you start with $1,000, deposit $100 every month, earn 5% annual interest compounded monthly, and run the plan for 10 years. The periodic rate is i = 0.05 / 12 ≈ 0.00416667, and the total number of periods is N = 12 × 10 = 120. The starting balance grows to 1,000 × (1.00416667)^120 ≈ $1,647.01. The deposit stream grows to 100 × ((1.00416667)^120 − 1) / 0.00416667 ≈ $15,528.24. The future value is therefore 1,647.01 + 15,528.24 = $17,175.25. Total contributions are 1,000 + 100 × 120 = $13,000, and interest earned is 17,175.25 − 13,000 = $4,175.25. The same steps, repeated with $200 per month, produce a noticeably larger future value; the difference between the two is the savings generated by the higher deposit.
Reading the Result: Contributions vs. Interest
Once the calculator shows a future value, three numbers matter. The first is the future value itself, which is what your balance would be at the end of the horizon if nothing else changed. The second is total contributions, which is the sum of your starting balance and every deposit you made. The third is interest earned, which is the future value minus total contributions, representing the growth produced by the account rather than by your deposits.
Splitting the result this way is what makes the gap between two scenarios legible. If doubling your monthly deposit pushes total contributions up by $12,000 but the future value up by $15,000, then about $3,000 of the extra savings came from interest on the additional deposits, not from the deposits themselves. That extra interest is the compounding reward for contributing earlier and more consistently, and it is the same effect that a guide on how to calculate savings growth with regular deposits walks through in more detail.
Why the Gap Between Two Scenarios Changes
Four inputs drive the savings gap: the deposit amount, the annual rate, the deposit frequency, and the number of years. The table below describes how changing each one moves the gap between two projections, all else equal. Exact figures depend on the numbers you enter, so use the Savings Calculator to produce the precise values for your own scenarios.
| Scenario change | Direction of the savings gap | Why it moves |
|---|---|---|
| Higher monthly deposit | Gap widens | Each extra dollar compounds over the remaining periods, so the larger stream leaves more money to earn interest. |
| Higher annual interest rate | Gap widens over time | A bigger rate magnifies the difference between two balances each period, and the effect compounds. |
| Longer time horizon | Gap widens | More periods give interest more chances to build on itself, so the same deposit difference ends up larger. |
| More frequent deposits (monthly vs. annual) | Gap widens slightly | Interest is calculated and added more often, so each new deposit starts earning sooner. |
| Lower starting balance | Gap shrinks in absolute terms | A smaller initial lump sum means less principal available to earn interest from day one. |
Frequency matters less than people often expect, but it is not zero. Switching from annual to monthly deposits at the same annual rate produces a slightly higher future value, because interest is credited twelve times a year rather than once. The calculator lets you switch the frequency directly so you can see the effect for your own numbers without re-deriving the formula.
Limits of the Estimate and When to Verify
The formula assumes an ordinary annuity, which means each deposit is added at the end of its compounding period. Real accounts behave differently in three common ways: fees reduce the balance, taxes on interest reduce the compounding effect, and the interest rate itself can change over a multi-year horizon. The estimate the calculator produces is therefore a clean projection of the math, not a forecast of what your specific bank account will show. For short horizons and stable rates, the model is very close to reality; for long horizons and variable rates, treat the number as a planning anchor rather than a promise.
Estimates are for general information only and are not financial advice. Actual returns depend on real account terms, fees, taxes, and rate changes, so verify any figure with a licensed professional before acting on it. The calculator runs entirely in your browser, so none of the numbers you enter leave your device, which means you can experiment freely with two or three scenarios without worrying about who might see the inputs.