Savings Interest Calculator (Daily Compounding)
See how cash grows when interest is compounded every day and you keep adding to it. Daily compounding applies interest on top of interest with each day that passes, so even modest APY and steady deposits can snowball. It’s helpful when comparing account offers, timing a short-term goal, or understanding how much faster growth can be with more frequent compounding.
The Savings Interest (Daily Compounding) Calculator lets you map a simple savings plan into a clear growth forecast—projecting future balance and the portion that’s pure interest. The goal is to choose the right account and contribution rhythm with confidence, see the payoff of consistency, and set realistic timelines for emergency funds, down payments, or any near-term savings target.
Project balance with deposits & APY — enter a starting balance, a monthly deposit, and an APY to see your future balance and total interest earned over your chosen time horizon.
We project growth using your APY. Because APY already includes compounding, we convert it to an equivalent monthly growth factor and apply deposits at month-end. Outputs show future balance and interest earned.
Year-by-year snapshot
| Year | End balance | Interest earned | Total contributions |
|---|---|---|---|
| 1 | $14,123.66 | $523.66 | $13,600.00 |
| 2 | $18,432.88 | $1,232.88 | $17,200.00 |
| 3 | $22,936.02 | $2,136.02 | $20,800.00 |
| 4 | $27,641.81 | $3,241.81 | $24,400.00 |
| 5 | $32,559.35 | $4,559.35 | $28,000.00 |
Deposits are modeled at month end. APY is converted to an equivalent monthly growth factor, which already reflects daily compounding.
Results interpretation
How it works
We treat APY as the effective annual yield that already incorporates compounding. To model monthly deposits, we convert APY to an equivalent monthly growth factor.
Formulas, assumptions, limitations
Monthly factor. m = (1 + APY)^(1/12). This matches a daily-compounding APY on an annual basis.
Future value. FV = start·m^n + deposit·((m^n − 1)/(m − 1)), where n = months.
Interest earned. FV − (start + deposit·n).
Deposit timing. We assume deposits occur at the end of each month (ordinary annuity). For beginning-of-month deposits, multiply the deposit term by m.
Scope. We model principal & interest only—no taxes, fees, or rate changes. Treat outputs as planning estimates.
Edge cases. If APY ≈ 0%, the math reduces to simple addition: FV ≈ start + deposit·n.
Use cases & examples
Start with $2,500, deposit $250/mo at 4.40% APY for 2 years. Track how compound growth boosts the cushion.
Seed $5,000 and deposit $400/mo for 3 years at 4.00% APY to estimate the down payment window.
Test 3.75% vs 4.75% APY on the same deposit plan to see the long-run lift from a better rate.
Savings interest FAQs
What’s the difference between APR and APY?
APR is a nominal rate; APY includes compounding. For savings, banks quote APY so yields compare fairly.
Why convert APY to a monthly factor?
Monthly deposits are easy to model with a monthly growth factor m = (1+APY)^(1/12). Over a year, this matches the APY’s growth.
Are deposits end-of-month or start-of-month?
We assume end-of-month. If your deposits hit at the start of the month, actual growth will be slightly higher.
Do you include taxes and fees?
No. We keep the math clean. For taxable accounts, net your interest by your marginal tax rate.
Can APY change over time?
Yes. Our model treats APY as constant. For variable rates, rerun scenarios with a few APY levels.
Is daily compounding handled?
Yes—APY already reflects the compounding basis. Converting to a monthly factor preserves the annual growth implied by APY.
Grow savings with intent: turning APY into a plan
A savings account looks simple—move money in, earn interest—but small choices compound into large differences. The key is to translate a quoted APY and a deposit habit into a concrete trajectory we can trust. Our calculator connects the dots, so we can forecast realistically and adjust inputs until the plan fits our goals and budget.
APY in plain language
APY—annual percentage yield—answers a single question: if a bank applied its compounding method all year long at the stated rate, what percent would the balance grow? That means APY already includes how often interest accrues (daily for most banks). When we convert APY to a monthly factor, we aren’t changing the promise; we’re just slicing the same annual growth into 12 compounding steps to align with monthly deposits.
Deposits: small levers, big outcomes
- Consistency beats intensity. A modest deposit done every month outperforms sporadic lump sums.
- Timing helps. Depositing at the beginning of the month gives each dollar an extra month to grow.
- Auto-transfer removes friction. We pay ourselves first and let the balance climb quietly.
Stress-testing the plan
Rates move. Budgets flex. We can run three scenarios—base, optimistic, conservative—and bracket what outcomes look like. If the plan still works in the conservative case, we’re positioned well. If not, we can raise deposits, extend the timeline, or shop for a higher APY.
Where this model fits—and where it doesn’t
Savings accounts and high-yield savings are perfect use cases. Certificates of deposit (CDs) and money market accounts behave similarly if we map their yields to APY. Investment accounts are different—market returns are volatile and not comparable to a fixed APY. For those, use our investment return tools designed for variable growth.
Practical playbook
- Pick a goal and date—emergency fund, vacation, down payment, tuition buffer.
- Choose a target APY. If we can move banks for a better yield, test that number.
- Back into the required monthly deposit. If it’s too high, extend the horizon or find rate improvements.
- Automate deposits and revisit quarterly. Small tweaks now keep us on track later.
The mathematics behind the scenes
Because APY is an effective annual rate, the equivalent monthly factor is m = (1 + APY)1/12. Over n months, a starting balance compounds to start · mⁿ. A stream of month-end deposits behaves like a geometric series, adding deposit · (mⁿ − 1)/(m − 1). Add the two and we get the future value. This closed-form solution is stable even for long horizons, and it aligns with how banks disclose APY.
What to watch in the real world
- Minimum balance tiers. Some banks pay different APYs above thresholds; use the lower tier for conservatism.
- Intro rates. Promotional APYs may drop after a period; model both promo and post-promo rates.
- Taxes. Interest in taxable accounts generally counts as ordinary income. If it matters, net the APY after tax.
- Inflation. Purchasing power changes. For long horizons, compare real growth by subtracting an inflation estimate.
Bottom line
We can’t control rates, but we can control deposits and discipline. By turning APY into a clear monthly trajectory, we make savings a system instead of a wish. The result is momentum—and a balance that shows it.