Future Value of Annuity Calculator — How Much Will Your Savings Grow?
Quick Guide: Enter your periodic payment amount, annual interest rate, annuity term, payment frequency, compounding frequency, and annuity type to calculate the future value of a series of equal payments. Perfect for retirement savings planning, college funds, investment accounts, and any regular savings goal.
What is an Annuity?
An annuity is a series of equal payments made at regular intervals over a defined period. Two conditions must be met:
- Equal payments: Every payment is the same amount.
- Fixed intervals: Payments occur at regular, predetermined times (monthly, quarterly, annually, etc.).
Annuities appear everywhere in personal finance:
- Retirement savings: Monthly contributions to a 401(k) or IRA
- Education funds: Regular deposits to a college savings account
- Investment plans: Systematic investment in mutual funds or bonds
- Mortgage/loan payments: Fixed monthly installments
- Insurance premiums: Regular premium payments
Types of Annuities
Payments are made at the end of each period. This is the most common type.
Examples: Mortgage payments, car loans, student loans, bond coupon payments.
Timeline (3 years):
Now → Period 1 → Payment 1 → Period 2 → Payment 2 → Period 3 → Payment 3
Payments are made at the beginning of each period. Because payments are invested one period earlier, the future value is higher than an ordinary annuity.
Examples: Rental lease payments, life insurance premiums, lottery payoffs, subscription services.
Timeline (3 years):
Payment 1 → Period 1 → Payment 2 → Period 2 → Payment 3 → Period 3
Payments increase at a constant rate each period — useful for modeling salary-linked contributions or inflation-adjusted savings.
Examples: Annual contributions that grow by 3% each year, salary-matched pension contributions.
Use the Growth Rate field in our calculator to model this scenario.
Fixed annuities provide a guaranteed rate of return — similar to a certificate of deposit. They offer security but may lose purchasing power due to inflation.
Variable annuities allow you to invest payments in market-linked assets (stocks, bonds). Returns fluctuate but can be significantly higher over the long term.
Equity-indexed annuities link returns to a market index (e.g., S&P 500) with a floor and cap on returns.
How to Use Our Future Value of Annuity Calculator
- Select Currency: Choose your currency (USD, RUB, EUR, GBP, and 16 more).
- Enter Payment Amount (PMT): The fixed amount you will invest each period.
- Set Interest Rate (r): Annual nominal interest rate as a percentage.
- Enter Term: Total duration of the annuity in years.
- Choose Payment Frequency (q): How often you make payments — annual, semi-annual, quarterly, or monthly.
- Select Compounding Frequency (m): How often interest compounds — annual, semi-annual, quarterly, monthly, or continuous.
- Pick Annuity Type: Ordinary (end of period) or Annuity Due (beginning of period).
- Optional Growth Rate (g): If your payments grow at a constant rate, enter it here.
- Click Calculate to see your future value instantly.
The Future Value of Annuity Formulas
Ordinary Annuity
FVA = PMT / i × ((1 + i)ⁿ − 1)
Where:
- FVA = Future Value of Annuity
- PMT = Payment amount per period
- i = Periodic interest rate = r / m (annual rate ÷ compounding frequency)
- n = Total number of periods = q × t (payment frequency × years)
Annuity Due
FVA = PMT / i × ((1 + i)ⁿ − 1) × (1 + i)
The annuity due formula multiplies the ordinary annuity result by (1 + i), reflecting that each payment compounds for one additional period.
Growing Annuity (g ≠ i)
FVA = PMT / (i − g) × ((1 + i)ⁿ − (1 + g)ⁿ)
Where: g = periodic growth rate of payments
Growing Annuity (g = i)
FVA = PMT × n × (1 + i)ⁿ⁻¹
Special case when the growth rate equals the interest rate.
Continuous Compounding (m → ∞)
FVA = PMT / (eʳ − 1) × (eʳᵗ − 1)
Where e ≈ 2.718 (Euler's number), r = annual interest rate, t = years.
Worked Examples
Example 1 — Ordinary Annuity: Retirement Savings
Scenario: You deposit $100 at the end of each year for 3 years. The interest rate is 5% annually.
- PMT = $100, r = 5%, t = 3 years, m = q = 1 (annual)
- i = 0.05, n = 3
FVA = 100 / 0.05 × ((1.05)³ − 1) = 2000 × 0.1576 = $315.25
Each payment compounds differently: Payment 1 earns interest for 2 years, Payment 2 for 1 year, Payment 3 earns none.
Example 2 — Annuity Due: Rental Payments Invested
Scenario: You invest $100 at the beginning of each year for 3 years at 5%.
FVA(due) = FVA(ordinary) × (1 + i) = $315.25 × 1.05 = $331.01
The annuity due is worth $15.76 more because every payment earns one extra period of interest.
Example 3 — Monthly Contributions: College Fund
Scenario: You save $200/month for 18 years at 6% annual rate, compounded monthly.
- PMT = $200, r = 6%, t = 18, m = q = 12
- i = 0.06/12 = 0.005, n = 18 × 12 = 216
FVA = 200 / 0.005 × ((1.005)²¹⁶ − 1) = 40,000 × 1.938 = ~$77,518
Total contributions: $200 × 216 = $43,200. Interest earned: ~$34,318.
Example 4 — Growing Annuity: Salary-Linked Pension
Scenario: You contribute $5,000/year, growing at 3%/year for 20 years. Interest rate is 7%.
- PMT = $5,000, r = 7%, g = 3%, t = 20, g ≠ i
- i = 0.07, n = 20
FVA = 5000 / (0.07 − 0.03) × ((1.07)²⁰ − (1.03)²⁰)
FVA = 125,000 × (3.8697 − 1.8061) = 125,000 × 2.0636 = ~$257,950
FAQs
You make a series of equal payments into an interest-bearing account. Each payment earns compound interest from the time it is made until the end of the annuity term. The future value is the total accumulated amount — your contributions plus all interest earned.
In an ordinary annuity, payments are made at the end of each period (e.g., month-end). In an annuity due, payments are made at the beginning of each period. Since annuity due payments are invested one period sooner, they earn one extra compounding period and produce a higher future value.
FVA(due) = FVA(ordinary) × (1 + i)
It depends on your financial goals and risk tolerance:
- Fixed annuities offer security and predictable returns but may lose purchasing power to inflation.
- Variable annuities can return significantly more but expose you to market risk.
- Annuities are most beneficial for long-term goals like retirement, where the power of compound interest has time to work.
Use your expected annual return rate. Common benchmarks:
- High-yield savings account: 4–5%
- Bond portfolio: 3–6%
- Balanced fund (stocks + bonds): 5–7%
- Stock index fund (long-term average): 7–10%
Be conservative — markets can underperform expectations. Always consult a financial advisor for major decisions.
More frequent compounding means interest is calculated and added to principal more often, generating interest on interest sooner. Monthly compounding at 6% yields slightly more than annual compounding at 6% because interest starts earning returns earlier each year.
Continuous compounding (m → ∞) uses e (Euler's number) and represents the theoretical maximum.
Future Value of Annuity (FVA) tells you how much your regular payments will be worth at a future date — useful for savings and investment planning.
Present Value of Annuity (PVA) tells you the current worth of a series of future payments — useful for evaluating pensions, loans, and settlement offers.
In a regular annuity, every payment is the same. In a growing annuity, payments increase by a constant percentage (the growth rate g) each period. This is useful when modeling contributions that grow with salary or inflation. Use the Growth Rate field in our calculator.
Ordinary Annuity vs. Annuity Due — Comparison
| Characteristic | Ordinary Annuity | Annuity Due |
|---|---|---|
| Payment Timing | End of period | Beginning of period |
| Future Value | Lower | Higher (multiplied by 1 + i) |
| Compounding Periods per Payment | n periods for first payment, 0 for last | n periods for first payment, 1 for last |
| Common Examples | Mortgages, car loans, bonds | Rent, insurance, lottery payouts |
| Formula Adjustment | Base formula | Multiply ordinary result by (1 + i) |
US and Metric Systems Note
This calculator works with any currency and any unit of time. Whether you use US dollars or Russian rubles, monthly or annual contributions, the same mathematical formulas apply. Simply select your preferred currency from the dropdown to see results in your local denomination.
Important Notes
- Results are based on mathematical formulas and assume a constant interest rate throughout the annuity term.
- Actual investment returns may vary due to market conditions, fees, and taxes.
- This tool is for educational and planning purposes only.
- Always consult a qualified financial advisor before making major financial decisions.