Quick Answer
Quick Answer: The calculator treats your rate as an APY -- the yield your bank advertises, which already includes compounding -- and converts it to the equivalent monthly rate. It then simulates your account month by month: each month it adds your deposit, then credits interest at that monthly rate on the previous month's closing balance. For $10,000 up front plus $500/month at 5% APY over 10 years, the engine returns $93,470.53 -- $70,000 of deposits and $23,470.53 of compound interest. The loop gives the same result as the closed-form future value formula shown on this page.
Key Takeaways
- The core calculation uses four inputs -- initial deposit, monthly contribution, annual rate (entered as an APY), and years
- The APY is converted to a monthly rate, i = (1 + APY)1/12 − 1, not divided by 12 -- dividing by 12 would compound a rate that is already compounded
- Interest is credited monthly by default; each deposit starts earning interest the month after it is made (the standard ordinary-annuity convention)
- At 5% APY, the default $10,000 + $500/month plan reaches $93,470.53 in 10 years -- interest contributes $23,470.53 of that
- The rate matters enormously: the identical plan earns $2,020.07 of interest at 0.5% APY but $23,470.53 at 5% APY
- Results are pre-tax and assume one constant rate -- real account rates move with Federal Reserve policy
The Savings Math in Plain English
A savings account with regular deposits grows from two forces: the money you add, and the interest the bank credits on your whole balance. The calculator models exactly that, one month at a time:
- Start with your initial deposit.
- Each month, add your contribution to the balance.
- Then credit one month of interest on the balance the account closed with last month, at the monthly rate that compounds to your APY over a year.
- Repeat for every month in the projection.
Because interest is credited on an ever-growing balance, the interest itself compounds: in the default 10-year example, the account earns far more interest in year 10 than in year 1, even though the rate never changes. That is why the deposits ($70,000) and the ending balance ($93,470.53) drift further apart the longer you save.
The rate is an input you choose -- enter the APY your account actually pays, exactly as the bank advertises it. Under the Truth in Savings Act, as implemented by the CFPB's Regulation DD(opens in new tab), banks generally must state the APY on deposit accounts, so it is usually the easiest rate to find. If you only have a nominal rate, convert it first with APY = (1 + nominal rate ÷ n)n − 1, where n is the number of compounding periods per year. Savings rates differ widely between traditional and high-yield accounts; our best savings rates guide tracks current offers, and deposits at FDIC-member banks are insured up to the limits described by the FDIC(opens in new tab).
The Mathematical Formula
Here is the exact math used by our Savings Calculator at its default settings (monthly deposits, interest credited monthly). The engine runs the month-by-month loop described above; that loop gives the same result as the closed future-value form:
FV = P × (1 + i)m + PMT × [ ((1 + i)m − 1) ÷ i ]
with the monthly rate and month count defined as:
i = (1 + r)1/12 − 1 m = years × 12
where r is the APY as a decimal. Because an APY already includes compounding, the monthly rate is the one that compounds back to r over twelve months: (1 + i)12 = 1 + r. Dividing r by 12 instead would treat it as a nominal rate and overstate the interest. The first term is the compound growth of your initial deposit; the second is the future value of the monthly deposit stream (an ordinary annuity -- each deposit earns interest from the month after it arrives). The engine also reports your total deposits and the interest earned:
Interest earned = FV − (P + PMT × m)
Variable Definitions
| Variable | Meaning | Units / How to Enter | Example ($10K, $500/mo, 5% APY, 10 yr) |
|---|---|---|---|
| P | Initial deposit | USD | $10,000 |
| PMT | Monthly contribution | USD per month | $500 |
| r | Annual rate, as an APY (annual percentage yield) | Percent per year as advertised by the bank, as a decimal in the formula | 5% = 0.05 |
| i | Monthly interest rate | (1 + r)1/12 − 1 | 0.0040741 |
| m | Number of months | Years × 12 | 120 |
| (1 + i)m | Compound growth factor | Raise (1 + monthly rate) to the power of m | 1.0040741120 = 1.628895 |
Valid Input Ranges
The calculator page accepts an initial deposit from $0 to $100,000,000, a monthly contribution from $0 to $1,000,000, an APY from 0% to 20%, and a horizon of 1 to 50 whole years. The underlying engine accepts rates up to 50%; the page's lower cap keeps entries in a realistic range for savings accounts.
Worked Example: $10,000 + $500/Month at 5% APY for 10 Years
This section walks through the closed-form arithmetic using the calculator's default inputs (5% APY, monthly deposits, interest credited monthly). You can follow along with a standard calculator and verify each number against our Savings Calculator, which rounds its display to whole dollars ($93,471 and $23,471).
Step 1: Convert the APY to a Monthly Rate
- APY = 5% = 0.05
- i = (1.05)1/12 − 1 = 0.0040741 (0.40741% per month)
Step 2: Compute the Compound Growth Factor
- Months = 10 × 12 = 120
- (1.0040741)120 = 1.0510 = 1.628895
Step 3: Grow the Initial Deposit
- $10,000 × 1.628895
- = $16,288.95
Step 4: Grow the Deposit Stream
- $500 × [(1.628895 − 1) ÷ 0.0040741]
- = $500 × 154.3632 (at full precision; the rounded inputs shown give about 154.364)
- = $77,181.58
Step 5: Add the Parts and Split Out Interest
- FV = $16,288.95 + $77,181.58 = $93,470.53
- Total deposited = $10,000 + ($500 × 120) = $70,000
- Interest earned = $93,470.53 − $70,000 = $23,470.53
Read together: you deposit $70,000 over the decade and the account credits $23,470.53 of compound interest on top. Every figure above was computed by the calculator's engine with inputs P = $10,000, PMT = $500, APY = 5, years = 10 (verified September 27, 2026); the engine's month-by-month simulation matches the closed form to within a fraction of a cent.
How the Interest Rate Changes the Result
The rate is the single biggest lever on the interest you earn. The table below holds the plan fixed ($10,000 initial, $500/month, 10 years, interest credited monthly) and varies only the APY. Every row was computed by the engine.
| Assumed APY | Ending Balance | Interest Earned |
|---|---|---|
| 0.5% | $72,020.07 | $2,020.07 |
| 1% | $74,106.69 | $4,106.69 |
| 3% | $83,163.16 | $13,163.16 |
| 4% | $88,150.41 | $18,150.41 |
| 5% (calculator default) | $93,470.53 | $23,470.53 |
The same $70,000 of deposits earns $2,020.07 at 0.5% APY but $23,470.53 at 5% APY -- more than eleven times as much, purely from where the money sits. This is the arithmetic behind moving cash to a higher-yielding account; see our best savings rates guide for what accounts currently pay.
Time Compounds It Too
Holding 5% APY fixed and varying the horizon (engine-computed): the same plan reaches $46,669.68 in 5 years, $93,470.53 in 10 years, $229,435.22 in 20 years, and $450,907.38 in 30 years. Over 30 years the interest ($260,907.38) exceeds the deposits ($190,000) -- the account earns more than you put in.
Deposit Timing and How This Differs From the Compound Interest Calculator
When Deposits Start Earning
In the engine's monthly loop, each deposit is added to the balance first, but the month's interest is credited on the previous month's closing balance -- so a deposit starts earning interest the month after it arrives. This is the standard ordinary annuity convention, and it is why the simulation and the closed-form formula agree exactly: the first deposit compounds for 119 of the 120 months, and the final deposit earns nothing.
Same Formula, Different Rate Convention
Our compound interest calculator uses the same future-value formula but reads the rate differently. It treats 5% as a nominal annual rate compounded monthly, so its monthly rate is 0.05 ÷ 12 = 0.0041667 -- an effective yield of about 5.12% a year. The savings calculator treats 5% as the APY itself. For the default plan the compound interest calculator therefore returns $94,111.23, while the savings calculator returns $93,470.53 (both engine-verified). Neither is wrong; they answer different questions. Use the savings calculator when you have an advertised APY and the compound interest calculator when you have a nominal rate.
What the On-Page Calculator Adds
The savings calculator page offers extra planning options that generalize the same monthly loop: deposit frequency (weekly, bi-weekly, monthly), how often interest is credited (daily, monthly, quarterly, annually), an annual increase in your contribution, and a delayed start. Because the rate is an APY, the crediting choice does not change what a balance left alone earns -- it changes how soon new deposits start earning. For the default plan, daily and monthly crediting both give $93,470.53, quarterly gives $93,156.93, and annual gives $91,756.30 (engine-computed). The worked example and tables on this page use the default settings: monthly deposits, monthly crediting, no annual increase, no delay.
Data Sources and Methodology Notes
Our Savings Calculator uses the month-by-month compounding math documented above. The engine carries full decimal precision through every intermediate step and rounds only the displayed figures.
Calculation Engine
The same engine code runs in the browser and behind the REST savings alias of our public calculator API (see the API reference), so those two give identical results. It returns the final balance, total contributions, and total interest earned. The MCP tool project_growth reads the rate as a nominal annual rate by default, the compound interest calculator's convention, so for the default plan it returns $94,111.23. Called with rate_type: "apy" (from contract 2.1.0) it runs this page's formula and returns $93,470.53, the same as this calculator. As a reproducibility check, the worked example and every table figure on this page were generated by the savings engine (verified September 27, 2026).
Reference Data
- The FDIC's deposit insurance resources(opens in new tab) explain the coverage that applies to insured savings deposits.
- Our best savings rates guide tracks the current rate environment so you can pick a realistic rate assumption.
Assumptions and Limitations
- The engine applies one constant APY for the whole projection, credited monthly by default. Real savings rates are variable and move with Federal Reserve policy.
- The figures on this page use monthly deposits with no annual increase and no start delay -- the calculator page's default settings. The on-page calculator offers additional deposit-frequency, crediting-frequency, step-up, and delay options.
- Results are pre-tax: interest on ordinary savings accounts is taxable income, which the engine does not model.
- Inflation is not applied; to translate a future balance into today's purchasing power, see our inflation calculator methodology.
- Accepted inputs on the calculator page: initial deposit $0-$100,000,000, monthly contribution $0-$1,000,000, APY 0%-20%, 1-50 whole years (the engine itself accepts rates up to 50%).
Check It Yourself
The question. You deposit $10,000 in an account paying 4.00% APY and leave it alone. How much do you have after one year, and after five?
Our answer. In the Savings Calculator, enter an initial deposit of $10,000, a monthly contribution of $0, an annual interest rate (APY) of 4% and a time period of 1 year. The future balance is $10,400, with $400 of interest. Change the time period to 5 years and the balance is $12,167. Switching compounding from monthly to daily doesn't change either figure, because the calculator treats the rate you enter as an APY, which already includes the effect of compounding.
The source. The Truth in Savings rule (Regulation DD), Appendix A(opens in new tab), defines the annual percentage yield banks must use: APY = 100 [(1 + Interest/Principal)(365/Days in term) − 1]. For a 365-day term this simplifies to APY = 100 × (Interest ÷ Principal), so a 4.00% APY means $400 of interest on $10,000 over a year.
Reproduce it.
- One year: $10,000 × 4.00% = $400 of interest, for a balance of $10,400. Check it against the formula: 100 × ($400 ÷ $10,000) = 4.00%.
- Five years at the same APY: $10,000 × 1.045 = $12,166.53.
In a spreadsheet, =10000*(1+0.04)^5 returns 12,166.53; the calculator shows $12,167, rounded to the dollar. This is the same APY-to-growth rule the worked example above uses for its $93,470.53 result, without the monthly deposits. The calculator holds your rate steady for the whole period; real savings rates can change, so treat multi-year figures as estimates. If your figure differs from ours, email admin@markcolabs.com with the inputs you used and the figure you got, and we'll compare it against the source.
Frequently Asked Questions
The engine treats the rate you enter as an APY (annual percentage yield, the yield after compounding) and converts it to the equivalent monthly rate, i = (1 + APY)1/12 − 1. It then simulates your account month by month: each month it adds your deposit, then credits interest at that monthly rate on the previous month's closing balance. Over 10 years, $10,000 up front plus $500/month at 5% APY grows to $93,470.53 -- $70,000 of deposits and $23,470.53 of interest. The month-by-month loop gives the same result as the closed-form future value formula FV = P(1+i)m + PMT × [((1+i)m − 1) ÷ i].
At a 5% APY with interest credited monthly, $500/month grows to $77,181.58 in 10 years -- $60,000 of deposits plus $17,181.58 of interest. Start with $10,000 already saved and the ending balance is $93,470.53. At lower rates the interest shrinks fast: the $10,000 + $500/month plan earns only $4,106.69 of interest at 1% APY.
In the engine, a deposit made in a given month starts earning interest the following month -- interest is always credited on the previous month's closing balance. This matches the standard ordinary-annuity convention, which is why the month-by-month simulation and the closed-form annuity formula agree to a fraction of a cent.
Use the APY your account actually pays, exactly as the bank advertises it -- savings account rates vary widely between traditional banks and high-yield online accounts, and they change with Federal Reserve policy. Our best savings rates guide tracks current offers. Because the rate is an assumption, it is worth running the calculation at a couple of rates to see the range of outcomes.
The formula has the same shape, but the two calculators read the rate differently, so the same inputs give slightly different answers. The savings calculator treats 5% as an APY, which already includes compounding: $10,000 plus $500/month for 10 years reaches $93,470.53. The compound interest calculator treats 5% as a nominal annual rate compounded monthly (i = 0.05 ÷ 12), which works out to an APY of about 5.12%, so the same plan reaches $94,111.23 there (both engine-verified). Use the savings calculator when you have an advertised APY and the compound interest calculator when you have a nominal rate.
Sources
- Federal Deposit Insurance Corporation -- Deposit Insurance(opens in new tab)
- Consumer Financial Protection Bureau -- Regulation DD (Truth in Savings), 12 CFR Part 1030(opens in new tab)
- U.S. Securities and Exchange Commission (Investor.gov) -- Compound Interest Calculator(opens in new tab)
- Consumer Financial Protection Bureau -- Planning for Retirement(opens in new tab)
Important Disclaimer
Disclaimer: This content is for educational and informational purposes only and does not constitute financial, tax, or investment advice. Individual circumstances vary, and you should consult with a qualified financial professional before making long-term financial decisions. Projections use a constant assumed interest rate; actual savings account rates are variable and change over time, so real outcomes will differ from any projection. While we strive for accuracy, economic data and conditions change over time. Data current as of September 2026.
Content reviewed by Mark at Markco Labs. Learn more about our accuracy standards.