Future Value of Annuity Due Calculator

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Reviewed by: Dr. Marcus Loehr, Actuarial Scientist
Dr. Loehr has 15 years of experience in insurance mathematics and advanced compound interest modeling for financial markets.

The **Future Value of Annuity Due (FVAD) 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) is calculated based on the assumption that all payments are made at the **beginning** of the period, allowing the payments to earn an extra period of interest compared to an ordinary annuity.

$$ FV = PMT \cdot \left[ \frac{(1+r)^N – 1}{r} \right] \cdot (1+r) $$ $$ PMT = \frac{FV \cdot r}{\left((1+r)^N – 1\right) \cdot (1+r)} $$ $$ N = \frac{\ln\left[1 + \frac{FV \cdot r}{PMT \cdot (1+r)}\right]}{\ln(1+r)} $$ $$ R \quad \text{(Solved Iteratively)} $$

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 due:

  • 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).

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Plan your savings and investments with these related financial tools:

What is Future Value of Annuity Due?

The **Future Value of Annuity Due (FVAD)** calculates the cumulative value of a stream of equal, scheduled payments made at the **beginning** of each period. Because the payment is deposited immediately at the start of the period, it earns interest for that entire period. This subtle difference makes the FVAD greater than the Future Value of an Ordinary Annuity (FVA), which deposits payments at the end of the period.

This model is often used in situations like rent payments, insurance premiums, or certain savings plans where contributions are made at the start of the month or year. The formula mathematically adjusts the FVA formula by multiplying the result by the compounding factor $(1+r)$ to account for the extra period of interest.

How to Calculate FVAD (Example)

  1. 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).

  2. Convert Rates to Decimal:

    Periodic rate ($r$) is $0.5\% / 100 = \mathbf{0.005}$.

  3. Calculate the FVA Factor:

    The ordinary annuity factor: $\left[ \frac{(1+r)^N – 1}{r} \right] \approx \mathbf{69.77003}$ (from step 3 of FVA calculation).

  4. Calculate FVAD:

    Multiply the FVA result by $(1+r)$: $$ FVAD = \$100 \times 69.77003 \times (1.005) \approx \mathbf{\$7,011.88} $$ The total amount accumulated is $\mathbf{\$7,011.88}$.

Frequently Asked Questions (FAQ)

Q: What is the main characteristic of an Annuity Due?

A: The main characteristic is that payments occur at the **beginning** of each period. This is crucial as it earns interest one period sooner than an ordinary annuity.

Q: Why is FVAD always higher than FVA?

A: FVAD is always higher because every payment is compounded for one additional period compared to an FVA, leading to greater total interest earned.

Q: Can I use this for calculating retirement savings?

A: Yes. If your retirement contributions (like 401k or IRA deposits) are made at the beginning of the month, FVAD provides a more accurate projection of your future nest egg.

Q: How do you calculate the total interest earned?

A: Total interest earned is the difference between the Future Value (FV) and the total principal paid over the life of the annuity: $I = FV – (PMT \cdot N)$.

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