Future Value of Annuity Calculator
Calculate the future value of annuities due, ordinary regular annuities, and growing annuities
For perpetuity, enter ‘p’, ‘P’, ‘perpetuity’ or ‘Perpetuity’
For continuous compounding, enter ‘c’, ‘C’, ‘continuous’ or ‘Continuous’
For non-growing annuity, enter 0
About This Calculator
This calculator helps you determine the future value of a series of annuity payments. It can calculate:
• Ordinary annuities (payments at end of period)
• Annuities due (payments at beginning of period)
• Growing annuities (with increasing payments)
• Perpetuities (infinite payment streams)
• Both discrete and continuous compounding
Future Value of Annuity Calculator
The Future Value of Annuity Calculator helps you determine how much a series of regular deposits will grow into at a future date, considering interest rates, compounding, and payment frequency. Whether you’re planning for retirement, saving for education, or building wealth systematically, this tool shows the exact accumulation of your annuity payments over time.
An annuity is simply a sequence of equal payments made at regular intervals. By applying time value of money principles, the calculator computes the future value (FV) — the total worth of those payments at a given point in the future.
What is the Future Value of an Annuity?
The future value of an annuity is the total amount accumulated when you invest a fixed payment on a recurring schedule, compounded at a given interest rate.
For example, if you invest $500 every month into a savings account that compounds interest monthly at 5% annually, the calculator determines what that series of deposits will be worth after, say, 20 years.
This is especially valuable for retirement planning, systematic investments, or understanding loan repayment structures. For quick single-deposit growth calculations, you can also try our Future Value Calculator.
Key Inputs in the Future Value of Annuity Calculator
1. Period
The “period” refers to the unit of time you’re measuring. A period is commonly a year, but it can also be a month, quarter, or any consistent interval.
2. Number of Periods (t)
This represents how long the payments will be made. For instance:
- 10 years annually → t = 10
- 5 years monthly → t = 60 periods
For a perpetuity (infinite series of payments), you can enter “p” or “Perpetuity.”
3. Interest Rate (R)
The nominal annual interest rate expressed as a percentage. For example, 6% → r = 0.06.
When compounding is not annual, the interest rate is adjusted for the compounding frequency.
4. Compounding (m)
The number of times interest compounds per period. Examples:
- Annually → m = 1
- Quarterly → m = 4
- Monthly → m = 12
- Daily → m = 365
If compounding is continuous, enter “c” or “continuous.”
For simpler one-off calculations without annuities, check our Future Value Calculator Basic.
5. Payment Amount (PMT)
The fixed amount invested or paid each period. For example, $200 every month.
6. Growth Rate (G)
Relevant only for growing annuities, this represents the percentage by which payments increase each period (e.g., matching inflation).
7. Payment Frequency (q)
This specifies how often payments occur within each period. Example:
- Annual payments → q = 1
- Monthly payments → q = 12
If payments are more frequent than compounding, the interest rate is converted to match.
8. Payment Timing (Type)
- 0 → Ordinary annuity (payments at the end of each period)
- 1 → Annuity due (payments at the beginning of each period)
Future Value of Annuity Formulas
Standard Formula
FV = PMT × [(1 + i)^n – 1] / i × (1 + iT)
Where:
- PMT = Payment per period
- i = Interest rate per compounding interval
- n = Total number of intervals
- T = 0 for ordinary annuity, 1 for annuity due
Future Value of an Ordinary Annuity
Payments at the end of each period:
FVordinary = PMT × [(1 + i)^n – 1] / i
Future Value of an Annuity Due
Payments at the beginning of each period:
FVdue = PMT × [(1 + i)^n – 1] / i × (1 + i)
Future Value of a Growing Annuity
If payments grow at rate g:
FV = PMT × [(1 + i)^n – (1 + g)^n] / (i – g)
Special Case: Growth Rate Equals Interest Rate
If g = i, the formula becomes:
FV = PMT × n × (1 + i)^(n – 1)
Continuous Compounding
If compounding is continuous:
FV = PMT × (e^(i × n) – 1) / (e^i – 1)
Example Calculations
Example 1: Ordinary Annuity
You invest $1,000 annually for 10 years at 5% interest, compounded annually.
FV = 1000 × [(1 + 0.05)^10 – 1] / 0.05
FV = 1000 × 12.5779
FV = $12,577.90
Example 2: Annuity Due
Same case, but payments are at the beginning of each year.
FV = 1000 × [(1 + 0.05)^10 – 1] / 0.05 × (1 + 0.05)
FV = 12,577.90 × 1.05
FV = $13,206.79
For multiple uneven cash flows, try our Future Value of Cash Flows Calculator.
Example 3: Growing Annuity
Payments start at $500 annually, grow at 3% per year, for 15 years, at 6% annual interest.
FV = 500 × [(1 + 0.06)^15 – (1 + 0.03)^15] / (0.06 – 0.03)
FV = $11,503.88
Growing annuities are ideal for retirement savings where contributions rise with income.
Special Cases
- Perpetuity: For t → infinity, FV also → infinity (if g < i).
- Continuous compounding with growth: Uses modified exponential formulas.
- Present vs. Future Value: Present value discounts cash flows back to today, while future value projects them forward.
For pure formula references, see our Future Value Formula Calculator.
Applications of Future Value of Annuity
- Retirement Planning – Estimate how much your regular contributions will grow into.
- College Savings – Project education funds with fixed deposits.
- Loan Repayments – See how payment schedules affect future costs.
- Business Finance – Evaluate systematic investment or reinvestment strategies.
For easy comparisons, use our Future Value Table of Annuities.
The Future Value of Annuity Calculator is a vital tool for projecting the growth of consistent investments or payments. With options for ordinary annuities, annuities due, and growing annuities, it adapts to real-world scenarios like retirement savings, loan structures, and investment planning.
By understanding how payment frequency, compounding, and growth rates influence results, you gain better control over your financial future. Explore related tools like our Future Value Investment Account Calculator or Future Value Investment Calculator for even more insights.