When you save the same amount on a fixed schedule — every month, every week — you are making an annuity. The future value of an annuity formula tells you what that stream of payments becomes after compounding. It is the mathematical engine behind our recurring deposit and savings goal calculators.

The Formula (Ordinary Annuity)

FV = PMT × [ ((1 + i)^n − 1) / i ]

Variable definitions

  • •**FV** = future value of the annuity.
  • •**PMT** = the payment made each period.
  • •**i** = the interest rate per period (the annual rate divided by the number of periods per year).
  • •**n** = the total number of payments.

This is an ordinary annuity: payments are made at the end of each period. The formula is a standard time-value-of-money result (see any introductory corporate-finance reference, and the SEC Investor.gov savings education materials).

Annuity Due (Payments at the Start)

If payments are made at the beginning of each period — an annuity due — each payment compounds for one extra period, so multiply the ordinary-annuity result by (1 + i):

FV_due = PMT × [ ((1 + i)^n − 1) / i ] × (1 + i)

Worked Example

Save PMT = $100 at the end of every month for 20 years at a 7% annual return compounded monthly. Here i = 0.07 / 12 = 0.0058333 and n = 12 × 20 = 240:

  1. Raise the factor: (1.0058333)^240 ≈ 4.0386.
  2. Subtract 1: 4.0386 − 1 = 3.0386.
  3. Divide by i: 3.0386 / 0.0058333 ≈ 520.88.
  4. Multiply by PMT: 520.88 × 100 ≈ $52,088.

You contributed $100 × 240 = $24,000, and roughly $28,088 of the final balance is compounded growth. Verify it with our recurring deposit calculator.

How It Connects to the Lump-Sum Formula

The annuity formula is the recurring-payment counterpart of A = P(1 + r/n)^(nt). A plan with both a starting balance and regular contributions simply adds the two results, which is exactly what the calculators on this site do.

Step-by-Step: Project a Recurring Contribution

  1. Pick the amount you can contribute each period (PMT) and be realistic.
  2. Convert the annual rate to a per-period rate: i = annual rate / periods per year.
  3. Count total payments: n = periods per year × years.
  4. Plug into FV = PMT × [((1 + i)^n − 1) / i].
  5. If payments are at the start of each period, multiply by (1 + i).
  6. Compare against the same plan in our calculator to confirm.

Note on vendor-specific parameters: a generic compound-interest or annuity formula is pure mathematics and does not depend on any bank, broker, fund, or product "tuning" parameters. There are no manufacturer- or vendor-specific coefficients to enter — only the universal variables (principal, rate, time, frequency, contribution). Product-specific terms (fees, APY caps, promotional rates) belong on the provider's disclosure, not in the formula.

<strong>Disclaimer:</strong> The content provided on CompoundFig is for educational and informational purposes only and does not constitute financial, tax, legal, or investment advice. All calculations and projections are hypothetical and based on assumed rates of return, which may not reflect actual market conditions. Historical figures cited here are factual records, not forecasts or guarantees of future performance. Individual results will vary. Consult a qualified financial professional before making decisions. CompoundFig does not provide personalized financial recommendations.

Sources & References

  • •U.S. Securities and Exchange Commission (Investor.gov) — saving and compound-growth education: investor.gov
  • •Standard future-value-of-annuity formula from introductory time-value-of-money / corporate finance.