Future value of a regular savings annuity, ordinary or due, with effective yield.
An annuity is the most common shape of long-term savings: a fixed payment made every period at a fixed interest rate, accumulating to a future balance. Pension contributions, monthly Roth-IRA deposits, plan d'épargne en actions (PEA) drips, sinking funds, and life-insurance premium streams all fit the annuity mould. The future value of an annuity is the canonical answer to "if I save X every month for Y years at Z %, what do I end up with?" — a question every household with a savings goal asks at least once a year. The arithmetic is closed-form so the answer is exact, not a Monte-Carlo estimate; what makes the calculation easy to mishandle is the choice of compounding frequency and the timing of payments (start of period vs end of period). This calculator pins both down explicitly and shows the accumulation curve so the contribution-vs-interest split is visible.
For an ordinary annuity (payment at the end of each period, the typical default), with payment P, periodic rate i, and N periods:
FV = P · ((1 + i)^N − 1) / i
For an annuity due (payment at the beginning of each period — common for rent, lease, and some pension schemes), multiply the ordinary annuity formula by (1 + i):
FV_due = FV_ordinary · (1 + i)
The periodic rate is the annual rate divided by the number of compounding periods per year: i = APR / n. The total number of periods is N = n × years.
The effective annual yield (APY) captures the actual annual return after compounding within the year:
APY = (1 + APR / n)^n − 1
When n = 1 the APY equals the APR. As n grows, APY climbs toward e^APR − 1 (continuous compounding); the practical jump from monthly to weekly is barely 0.01 % at typical rates.
When the rate is exactly zero the formula degenerates and you get the contributions back: FV = P · N. The calculator handles this edge case so a 0 % rate is meaningful (think a sock-under-the-mattress saving plan).
Enter the payment per period in your local currency. Enter the annual interest rate as a percentage. Pick the payments / compounding per year: yearly, semi-annual, quarterly, monthly, bi-weekly, or weekly. Enter the number of years you plan to keep saving. Choose annuity type: ordinary if the payment is made at the end of each period (the common default for savings plans), or annuity due if at the beginning (typical for prepaid rent, some pensions, or prélèvement automatique on the 1st of the month with same-month value).
The result panel shows the future value as the headline number, the total contributed across the savings horizon, the interest earned (the difference), and the effective annual yield implied by the compounding choice. The chart plots the accumulation curve in solid red and the contributions baseline in dashed green so the gap (interest earned, the magic of compounding) is visible across years.
€ 200 monthly for 30 years at 6 % APR, monthly compounding, ordinary annuity.
If the same plan is paid as an annuity due (start of month), multiply FV by 1.005 → € 201 906, an extra € 1 004 from earning one extra month's interest on every contribution.
APR vs APY confusion. A "5 % rate" can mean two very different things. APR is the nominal stated rate; APY is what you actually earn after intra-year compounding. A 5 % APR compounded monthly is 5.116 % APY; quoted as "5 % APY" the nominal rate is lower (4.889 %). Always check which you've been given.
Compounding frequency mismatch. If you contribute monthly but the account compounds quarterly, the calculation needs to be modeled as quarterly compounding with a stream of three payments per quarter. The simplification of "monthly contribution / monthly compounding" is a small error in most practical cases (≤ 0.05 % over 30 years) but it exists. Most retail savings products compound at the contribution frequency or daily.
Inflation is not modeled. Future-value numbers are in nominal currency. € 200 000 in 30 years at 2 % inflation is the equivalent of about € 110 000 today. For real-purchasing-power planning, subtract expected inflation from the rate before plugging in (use real rate ≈ nominal − inflation).
Tax drag inside taxable accounts. The calculator gives gross future value. In a taxable account, dividends, interest, and capital gains realized along the way are taxed annually — at a 30 % effective rate, the realized portion of returns is reduced. Tax-sheltered accounts (401(k), IRA, PEA, assurance-vie) more closely match the gross calculation.
Variable rates. Real-world fixed-rate savings products are rare beyond 5–10 years. Variable rates make the future value path-dependent: same average rate, different sequences, different ending balance. The calculator's flat-rate assumption is a planning estimate, not a contract.
Survivorship gap (life annuities). A "life annuity" pays out while you are alive; the future-value framing here is for accumulation annuities, not payout. Life-annuity pricing requires mortality tables and is not what this calculator does.
Periodic vs continuous compounding. For internal-finance comparisons across products with different compounding frequencies, convert everything to APY first.
Contribution timing within the period. The end-of-period assumption matters less when payments are weekly than when they are annual; for annual contributions, the start-of-year (annuity due) variant earns one extra year of compounding on every payment, which can lift FV by 5–10 % over a long horizon.