Dr. Vance specializes in time value of money analysis, annuity valuation, and advanced debt modeling.
The **Future Value of Annuity Due Calculator** determines the total accumulated value of a series of equal payments made at the **beginning** of each period, earning compound interest. This versatile four-variable calculator solves for any missing input: **Future Value ($FV$)**, **Periodic Payment ($PMT$)**, **Interest Rate ($R$)**, or the **Number of Periods ($N$)**. **Input any three of the four core variables** to find the missing one.
Future Value of Annuity Due Calculator
Future Value of Annuity Due Formulas
The Future Value of an Annuity Due (FVAD) formula is the standard future value of annuity formula multiplied by the compounding factor $(1+r)$ to account for payments made at the beginning of the period.
Note: $r$ is the decimal rate per period ($R_{percent}/100$).
Formula Source: Investopedia: Annuity Due
Variables Explained
The calculation relies on these four core Time Value of Money variables for annuities:
- Future Value (FV): The total balance accumulated after all payments and interest are calculated ($).
- Periodic Payment (PMT): The amount of the fixed, regular payment made at the beginning of each period ($).
- Interest Rate (R): The periodic interest rate applied, typically annual or monthly (%).
- Number of Periods (N): The total number of payments or compounding periods (e.g., months, years).
Related Calculators
Plan your savings and investments with these related financial tools:
- Future Value of Annuity (Ordinary) Calculator
- Present Value of Annuity Due Calculator
- Simple Interest Calculator
- Effective Annual Rate Calculator
What is Future Value of Annuity Due?
The **Future Value of Annuity Due (FVAD)** calculates the cumulative value of a series of payments made at the start of each period, including the interest earned on those payments. The “Annuity Due” distinction is critical: because payments are made at the beginning of the period, they earn one extra period of interest compared to an ordinary annuity (where payments are at the end). This slight difference results in a higher final future value.
This model is commonly used for retirement plans, rental payments, or any scenario where funds are deposited or withdrawn at the start of a cycle. This calculator helps investors visualize and plan their future wealth targets based on consistent upfront contributions.
How to Calculate FVAD (Example)
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Identify Components:
You deposit a $\mathbf{PMT}$ of $\mathbf{\$100}$ at the beginning of every month for $\mathbf{N}$ of $\mathbf{5 \ years}$ (60 periods). The monthly $\mathbf{R}$ is $\mathbf{0.5\%}$ (6% Annual).
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Convert Rates to Decimal:
Periodic rate ($r$) is $0.5\% / 100 = \mathbf{0.005}$.
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Calculate the Annuity Factor:
The standard annuity factor is calculated: $\left[ \frac{(1.005)^{60} – 1}{0.005} \right] \approx \mathbf{69.77003}$
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Calculate FVAD:
Multiply the annuity factor by PMT and the “due” factor ($1+r$): $$ FV = \$100 \times 69.77003 \times (1.005) \approx \mathbf{\$7,016.89} $$ The total amount accumulated is $\mathbf{\$7,016.89}$.
Frequently Asked Questions (FAQ)
A: In an **Annuity Due**, payments occur at the *beginning* of the period, allowing the payment to immediately earn interest. In an **Ordinary Annuity**, payments occur at the *end* of the period, so the last payment earns no interest, resulting in a slightly lower FV.
A: Yes. Many consumer loans (like mortgages and car loans) use the annuity due calculation for their final payment structure, as the payment is due immediately upon funding or at the start of the cycle.
A: The formulas for PMT, FV, and N are derived directly from the core time value of money equation. However, the equation must be solved for the rate ($r$) numerically, typically using iterative methods like the Newton-Raphson or binary search, as there is no closed-form algebraic solution.
A: Total interest earned is the Future Value ($FV$) minus the total amount paid. The total amount paid is simply the Periodic Payment ($PMT$) multiplied by the Number of Periods ($N$).