Expert in actuarial science, long-term savings strategies, and the compounding effects of regular contributions.
The **Future Value of Annuity Calculator** determines the total value of a series of equal payments (an annuity) at a specific future date, factoring in compound interest. This tool is essential for planning retirement savings, college funds, and regular investment contributions. It can also solve for the missing variable: Regular Payment, Future Value, Interest Rate, or Number of Periods.
Future Value of Annuity Calculator
Instructions: Enter values for any three of the four parameters (P, F, V, Q) to solve for the missing one.
Annuity Parameters
Future Value of Annuity Formula
The calculation uses the Annuity Factor, which changes based on payment timing ($t=0$ for Ordinary, $t=1$ for Due):
Ordinary Annuity (Payment at End of Period):
$$FV_{OA} = Pmt \times \left[ \frac{(1 + i)^N – 1}{i} \right]$$Annuity Due (Payment at Beginning of Period):
$$FV_{AD} = Pmt \times \left[ \frac{(1 + i)^N – 1}{i} \right] \times (1 + i)$$ Formula Source: Investopedia: Future Value of AnnuityVariables Explained (P, F, V, Q – Parameters)
- $Pmt$ (Regular Payment, $P$): The fixed amount deposited or received each period.
- $FV$ (Future Value, $F$): The total accumulated value of all payments plus interest at the end of the term.
- $i$ (Periodic Rate, $V$): The interest rate per compounding period (e.g., monthly rate if payments are monthly).
- $N$ (Number of Periods, $Q$): The total number of payments or compounding periods.
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What is Future Value of Annuity?
The **Future Value of Annuity (FVA)** is the accumulated value of a stream of equal, periodic payments, assuming a specified interest rate is earned on the investment. Annuities are common in personal finance, representing structured savings plans like 401(k) contributions, fixed deposits, or life insurance premium payments. The FVA calculation helps project how much a consistent savings habit will be worth in the future.
There are two types: an **Ordinary Annuity**, where payments occur at the end of the period (more common for mortgages or loans), and an **Annuity Due**, where payments occur at the beginning of the period (more common for rent or structured savings contributions). Annuity Due always results in a higher FVA because each payment compounds for one additional period.
How to Calculate Future Value of Annuity (Example)
You deposit \$100 ($Pmt$) at the end of every month for 5 years ($N=60$). The interest rate is 6% APR, compounded monthly ($i = 0.5\%$). We are solving for $FV_{OA}$:
- Step 1: Determine the Periodic Rate ($i$) and Periods ($N$)
$i = 6\% / 12 = 0.5\% = 0.005$. $N = 5 \times 12 = 60$ months.
- Step 2: Calculate the Future Value Annuity Factor
$\text{Factor} = \left[ \frac{(1 + 0.005)^{60} – 1}{0.005} \right] \approx 69.77003$
- Step 3: Solve for Future Value
$FV_{OA} = \$100 \times 69.77003 \approx \mathbf{\$6,977.00}$.
The total value of your savings after 5 years will be \$6,977.00. (Note: Total contributions were only \$6,000).
Frequently Asked Questions (FAQ)
Ordinary Annuity payments are made at the end of the period. Annuity Due payments are made at the beginning. Annuity Due generally yields a higher future value because the money is invested sooner.
The calculation must align the interest rate with the payment frequency. If payments are monthly, the rate must be the monthly rate ($APR/12$).
Compound Interest calculates the future value of a single lump sum. FVA calculates the future value of a series of lump sums, each growing via compound interest.
Yes, by entering the desired Future Value ($F$), Rate ($V$), and Periods ($Q$), the calculator can solve for the Regular Payment ($P$) needed to achieve the goal.