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Formula and help

Regular Savings Interest 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 Regular Savings Interest Calculator estimates how a starting balance and fixed monthly deposits could grow under one annual rate assumption. Enter the starting balance, monthly deposit, annual interest rate, and term in months to see final balance, total deposits, and gross interest earned.

Use this calculator when you want a focused regular-savings estimate with the same deposit every month and no tax, fee, withdrawal, inflation, or changing-rate model. Use the broader savings calculator when deposits can grow or tax-rate assumptions matter, and use the interest calculator when contribution timing or compounding frequency needs more control.

Formula notes

This formula page covers the app's Regular Savings Interest Calculator: one starting balance, one fixed monthly deposit, one annual percentage-rate assumption, and a term entered in months. It estimates gross savings growth before tax, fees, withdrawals, changing rates, provider rules, or personal tax treatment.

r = annualRatePct / 100 / 12; g = (1 + r)^n; depositGrowth = r === 0 ? D * n : D * ((g - 1) / r); FV = P * g + depositGrowth; TD = P + D * n; I = FV - TD

The annual percentage input is converted to a monthly decimal rate. The starting balance grows for every month, and fixed monthly deposits are treated as end-of-month deposits.
SymbolMeaningHow this page uses it
FVFinal balanceThe estimated ending balance after starting-balance growth and monthly deposits are combined.
PStarting balanceThe Starting balance entered on the calculator.
DMonthly depositThe fixed deposit added at the end of each month. The calculator does not increase this amount over time.
annualRatePctAnnual rate percentageThe Annual interest rate field as entered by the user, such as 4.25 for 4.25 percent.
rMonthly decimal rateThe annual percentage divided by 100 and then by 12. For 4.25 percent, r is about 0.00354167.
nTerm monthsThe Term in months field, used directly as the number of monthly growth periods.
gGrowth factorOne plus the monthly rate, raised to the term-month count.
depositGrowthEnd-of-month deposit growthThe future value of the fixed monthly deposits. When r is 0, this is simply deposits times months.
TDTotal depositsStarting balance plus all fixed monthly deposits made during the term.
IInterest earnedFinal balance minus total deposits, before tax, fees, or withdrawal effects.

Step by step

  1. Convert the entered annual percentage rate into a monthly decimal rate by dividing by 100 and then by 12.
  2. Raise one plus the monthly rate to the term-month count to calculate the growth factor for the starting balance.
  3. Grow the starting balance by multiplying it by that growth factor.
  4. Calculate the future value of fixed monthly deposits using the end-of-month annuity factor. The first monthly deposit earns interest for one fewer month than the starting balance.
  5. If the monthly rate is 0, skip the annuity division and use monthly deposit times term months for the deposit-growth piece.
  6. Add starting-balance growth and deposit growth to get Final balance.
  7. Calculate Total deposits as starting balance plus monthly deposit times term months.
  8. Calculate Interest earned as Final balance minus Total deposits.
  9. Choose the jurisdiction note from the calculation context: US examples say the projection is before federal or state tax, while UK examples say it is before PSA or tax treatment.
  10. Round currency outputs to two decimals after the full-precision growth calculation.

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, account-disclosure assumptions, bonuses, fees, or product-specific 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, 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, provider comparisons, or jurisdiction-specific product claims.

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

Assumptions

  • The starting balance, monthly deposit, annual rate, and term in months stay fixed for the whole projection.
  • Monthly deposits are modeled at month end. The calculator does not model beginning-of-month deposits, skipped deposits, deposit caps, withdrawals, rate changes, fees, bonus rates, inflation, provider rules, or live savings products.
  • Results use the numbers entered on the page, round currency outputs to two decimals, and are educational gross estimates rather than financial, tax, legal, lending, investment, provider, or regulated advice.

Formula version 2026.05.20-us-uk-gross-savings

Common mistakes to avoid

  • Treating the entered annual rate as a real APY, AER, product quote, or bank-rate promise. The calculator only uses the rate you enter as a planning assumption.
  • Comparing regular saver accounts without checking deposit limits, withdrawal rules, variable-rate terms, bonus-rate conditions, tax treatment, and whether the provider displays gross rate, AER, or APY.
  • Expecting tax or account-wrapper treatment in the result. US labels are before federal or state tax, and UK labels are before Personal Savings Allowance, ISA, or other tax treatment.

Worked example

Default example: $5,000 plus $250 monthly at 4.25 percent for 60 months

The default US and UK fixtures use a 5,000 starting balance, a 250 monthly deposit, a 4.25 percent annual-rate assumption, and a 60-month term.

  1. Convert 4.25 percent to 0.0425, then divide by 12 to get a monthly decimal rate of about 0.00354167.
  2. Raise 1.00354167 to the 60th power to get a growth factor of about 1.236302.
  3. The starting balance grows to about 6,181.51 before adding the future value of deposits.
  4. The end-of-month deposit factor gives about 16,680.13 of deposit value from 60 monthly deposits of 250.
  5. Final balance is 6,181.51 plus 16,680.13, which rounds to 22,861.64.
  6. Total deposits are 5,000 plus 250 times 60, or 20,000.00.
  7. Interest earned is 22,861.64 minus 20,000.00, or 2,861.64.
  8. The zero-rate validation case uses a 1,250 starting balance, 400 monthly deposits, and 24 months. Because r is 0, final balance equals total deposits of 10,850.00 and interest earned is 0.00.

The example explains the calculator mechanics. It is a gross educational estimate, not a bank quote, tax calculation, product comparison, or recommendation about where to save.

What this formula does not include

  • The annual rate is a user-entered planning assumption, not a live savings rate, bank quote, advertised APY, advertised AER, or provider disclosure.
  • The formula converts the entered annual percentage to a simple monthly rate by dividing by 12. It does not reverse-engineer product APY, AER, daily interest, bonus-rate, or promotional-rate disclosures.
  • Monthly deposits are fixed and modeled at month end. The calculator does not model beginning-of-month deposits, irregular deposits, skipped deposits, deposit caps, withdrawals, or contribution increases.
  • Results are gross before tax, fees, early-withdrawal effects, account charges, inflation, and product restrictions.
  • US and UK labels provide context only. The calculator does not apply federal tax, state tax, Personal Savings Allowance, ISA rules, reporting rules, withholding, or account-wrapper treatment.
  • No provider terms, minimum balances, eligibility rules, rate-change rules, deposit insurance limits, or account-protection claims are included.
  • Scoped independent comparator checks currently pass 4 of 4 scoped monthly-compounding, zero-tax, whole-year scenarios. The app-only jurisdictionNote output has no independent comparator equivalent, and validation maps this app's month input to whole-year terms where needed.
  • Currency outputs are rounded to two decimals after full-precision growth is calculated.

Terms used in this calculator

Gross interest
Interest before tax, fees, or deductions. The calculator reports gross interest so the formula stays separate from personal tax status and account-specific rules.
End-of-month deposit
A deposit modeled after that month's interest step. This means the first monthly deposit earns interest for one fewer month than the starting balance.
Annual rate assumption
The yearly percentage rate entered in the calculator. The model divides this by 100 and 12; it does not convert, verify, or compare real APY, AER, or product-rate disclosures.

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