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Formula and help

Savings Calculator Formula and Help

Learn how this calculator works, what formula it uses, and which assumptions sit behind the estimate.

Educational estimate, not financial advice.

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How it works

The Savings Calculator estimates how an initial deposit plus annual and monthly contributions could build under one fixed interest-rate assumption. It supports yearly contribution increases, several compounding frequencies, and a user-entered tax-rate drag so you can see the ending balance, total contributions, credited interest, and estimated tax paid.

Use this calculator when deposits can grow over time, when annual and monthly contributions both matter, or when you want to test a flat tax-rate assumption. Use the regular savings interest calculator for a simpler fixed monthly-deposit model, the interest calculator when contribution timing or inflation adjustment matters, the compound interest calculator for principal-only growth, and the CD calculator for fixed-term deposit examples.

Formula notes

This formula page covers the app's Savings Calculator: a month-by-month savings-growth simulation with an initial deposit, annual and monthly contributions, optional yearly contribution increases, a nominal interest-rate assumption, compounding frequency, and a user-entered tax-rate drag. It does not look up live savings rates, account rules, product fees, tax allowances, deposit insurance limits, or provider terms.

m = (1 + r / n)^(n / 12) - 1; continuous: m = e^(r / 12) - 1; B_t = B_(t-1) + interest after tax + deposits

The annual percentage rate is converted to an effective monthly rate. Each month credits after-tax interest first, then adds any monthly deposit, and adds the annual deposit at the end of each savings year.
SymbolMeaningHow this page uses it
B_tBalance after month tThe running savings balance after credited interest and any end-of-period deposits for that month.
PInitial depositThe Initial deposit entered on the calculator.
rNominal annual rate as a decimalThe Interest rate field divided by 100, so 3 percent becomes 0.03.
nCompounding periods per yearThe period count implied by the selected compounding frequency, such as 1 for annual, 12 for monthly, or 365 for daily.
mEffective monthly rateThe rate applied to the balance in each monthly simulation step after the compounding-frequency conversion.
TTotal monthsThe Years to save field multiplied by 12 and rounded to a whole month count.
AAnnual contributionThe first-year annual deposit, added at the end of months 12, 24, 36, and so on.
g_AAnnual contribution growthThe Annual contribution increase field. Each savings year scales the annual contribution by this percentage.
CMonthly contributionThe first-year monthly deposit, added after monthly interest is credited.
g_CMonthly contribution growthThe Monthly contribution increase field. Each savings year scales the monthly contribution by this percentage.
taxTax-rate assumptionThe user-entered percentage used to reduce credited monthly interest. It is not an official tax calculation.
TCTotal contributionsThe sum of annual and monthly deposits made during the simulation. It does not include the initial deposit.
I_netAfter-tax interestThe credited interest added to the balance after the tax-rate assumption is applied.
TaxEstimated tax paidThe simulated monthly interest tax that is not credited to the balance, accumulated across the term.

Step by step

  1. Convert the entered annual percentage rate into decimal form by dividing by 100.
  2. Convert the selected compounding frequency into an effective monthly rate. Continuous compounding uses e raised to the annual decimal rate divided by 12, minus 1.
  3. Convert the years-to-save input into a whole number of monthly simulation steps.
  4. At the start of each simulated month, calculate the savings year index so yearly contribution increases can be applied.
  5. Calculate monthly gross interest from the current balance and effective monthly rate.
  6. Apply the user-entered tax-rate assumption to that monthly gross interest, add the after-tax interest to the balance, and add the tax amount to Estimated tax paid.
  7. Add the monthly contribution after interest has been credited. If a monthly contribution increase is entered, scale the monthly contribution by the savings year index.
  8. At the end of each twelfth month, add the annual contribution. If an annual contribution increase is entered, scale the annual contribution by the savings year index.
  9. Return ending balance, initial deposit, total contributions excluding the initial deposit, after-tax interest credited to the balance, and estimated tax paid.
  10. Round currency outputs to two decimals after the full simulation is complete.

Sources and validation

This calculator is an original implementation based on documented formulas, app-specific assumptions, deterministic fixtures, edge cases, rounding policy tests, and internal validation. It is not copied from a single source.

Outputs are checked with deterministic fixtures, edge cases, rounding policy tests, and internal independent comparator checks where overlapping outputs are available. The result remains an educational estimate, not a quote, approval, tax answer, or personalised advice.

  • CFPB Regulation DD Appendix A should be used before copy discusses US annual percentage yield disclosure calculations, advertised APY terminology, bonuses, fees, average daily balance methods, or product-specific account-yield claims.
  • IRS Topic 403 and relevant state tax-authority materials should be used before copy discusses US taxable interest, reporting, withholding, tax-exempt interest, state tax, or personal tax outcomes.
  • GOV.UK Tax on savings interest, HMRC materials, and relevant UK tax guidance should be used before copy discusses Personal Savings Allowance, starting rate for savings, ISA treatment, joint-account interest, foreign savings, or UK tax payment rules.
  • FCA, MoneyHelper, provider disclosures, FDIC, FSCS, bank terms, BLS, ONS, and relevant local regulators should be used before copy discusses AER, gross or net savings rates, variable rates, promotional rates, account protection, eligibility, withdrawal limits, deposit caps, inflation, provider comparisons, or jurisdiction-specific product claims.

See the Calcs.finance methodology for the full review approach.

Assumptions

  • Initial deposit, annual contribution, monthly contribution, contribution-increase rates, interest rate, compounding frequency, years, and tax rate follow the values entered on the page for the whole projection.
  • Contributions are modeled at period end: monthly deposits are added after that month's interest step, and annual deposits are added after every twelfth month. The calculator does not model beginning-period deposits, skipped deposits, withdrawals, or changing deposit schedules beyond the entered yearly increases.
  • The tax rate is a flat user-entered assumption applied to monthly interest. The calculator does not look up official tax rules, allowances, CPI data, live APY or AER, provider rates, account fees, deposit insurance, withdrawal rules, promotional terms, product limits, or personal tax treatment, and results remain educational estimates rather than financial, tax, legal, lending, investment, provider, or regulated advice.

Formula version 2026.05.22-generic-savings-growth-simulation

Common mistakes to avoid

  • Treating Total interest earned as gross interest. In this calculator it is the interest credited after the entered tax-rate assumption; Estimated tax paid is tracked separately.
  • Comparing savings accounts from the result without checking whether a provider quotes APY, AER, gross rate, net rate, variable rate, bonus conditions, withdrawal limits, deposit caps, fees, or tax wrapper rules.
  • Assuming the contribution-increase fields add a one-time increase. They are yearly growth assumptions used when the model reaches a new savings year.

Worked example

Default example: $20,000 plus growing yearly deposits at 3 percent for 10 years

The default calculator inputs use a $20,000 initial deposit, $5,000 annual contributions that grow by 3 percent per year, no monthly contributions, a 3 percent nominal annual rate compounded annually, 10 years, and a 0 percent tax-rate assumption.

  1. Convert 3 percent to 0.03.
  2. With annual compounding converted into monthly simulation steps, the effective monthly rate is about 0.2466 percent.
  3. Run 120 monthly steps because the term is 10 years.
  4. Credit after-tax interest first each month. With a 0 percent tax assumption, all credited interest is kept in the balance.
  5. Add the first $5,000 annual contribution at the end of month 12, then grow later yearly contributions by 3 percent.
  6. Across the 10 years, the deposits made after the initial deposit add up to $57,319.40.
  7. The simulation ends with $92,116.99: the $20,000 initial deposit, $57,319.40 of later contributions, and $14,797.59 of after-tax credited interest.
  8. Estimated tax paid is $0 because the example uses a 0 percent tax-rate assumption.

This is a deterministic savings estimate from the entered assumptions. It can show how deposit habits, contribution increases, compounding, and tax drag interact, but it is not a bank quote, tax answer, or promise of an account outcome.

What this formula does not include

  • The interest rate is a user-entered assumption, not a live savings rate, advertised APY, AER, or provider quote.
  • The tax-rate field is a simple user-entered drag on monthly interest and does not apply official tax allowances, account wrappers, reporting rules, or jurisdiction-specific treatment.
  • Total interest is after-tax credited interest. Estimated tax paid is tracked separately and is not included in the total interest output.
  • Total contributions excludes the initial deposit; it only counts annual and monthly deposits made during the simulation.
  • Deposits are modeled as end-of-period additions after monthly interest is credited.
  • No withdrawals, fees, changing rates, promotional periods, minimum-balance rules, withdrawal limits, deposit insurance limits, provider terms, or inflation adjustment are modeled.
  • Currency outputs are rounded to two decimals after the full simulation is calculated.

Terms used in this calculator

Effective monthly rate
The monthly growth rate derived from the nominal annual rate and selected compounding frequency. This lets annual, monthly, daily, and continuous compounding feed the same monthly simulation.
After-tax credited interest
The part of monthly gross interest left after applying the tax-rate assumption entered in the calculator. The calculator adds this credited amount to the balance and reports estimated tax paid separately.
End-of-period contribution
A deposit added after that period's interest step. Monthly deposits are added after monthly interest; annual deposits are added after every twelfth month.

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