Future Value of Annuity Due Calculator

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Reviewed by: Dr. Helena V. Patel, Certified Financial Planner (CFP)
Dr. Patel is a CFP with 15 years of experience specializing in retirement planning, compound interest, and time value of money calculations.

The **Future Value of Annuity Due Calculator** is crucial for retirement and investment planning, as it calculates the future worth of a series of payments made at the *beginning* of each period. This 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 Annuity Due (FVAD) formula is derived from the ordinary annuity formula, multiplied by a factor of $(1+r)$ to account for the payments being made at the beginning of each period.

$$ FV = PMT \left[ \frac{(1+r)^N – 1}{r} \right] (1+r) $$ $$ PMT = \frac{FV \times r}{((1+r)^N – 1)(1+r)} $$ $$ N = \frac{\ln\left(1 + \frac{FV \cdot r}{PMT(1+r)}\right)}{\ln(1+r)} $$ $$ r \quad \text{Solve for } r: \quad FV = PMT \left[ \frac{(1+r)^N – 1}{r} \right] (1+r) $$

Formula Source: Investopedia: Annuity Due

Variables Explained

The calculation relies on these four core Time Value of Money variables:

  • Future Value (FV): The accumulated total value of all payments plus compounded interest at the end of the term ($).
  • Periodic Payment (PMT): The fixed amount paid or contributed at the beginning of each period ($).
  • Interest Rate (R): The interest rate earned per compounding period (e.g., if annual rate is 12% and compounded monthly, R=1%).
  • Number of Periods (N): The total number of payments/periods in the term (e.g., 5 years compounded monthly is 60 periods).

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What is Future Value of Annuity Due?

The **Future Value of Annuity Due** refers to the value of a series of equal payments made at the start of each period, including the interest compounded over time. Since payments are made earlier (at the beginning of the period), they have more time to earn interest compared to an ordinary annuity (payments at the end of the period). This small difference significantly increases the final future value, especially over long periods or at high interest rates.

This type of calculation is commonly used in long-term savings plans like Retirement Accounts (401k or IRA) where contributions are often deducted from a paycheck at the beginning of the month, or when calculating the final payout of a cash sweepstakes or structured settlement where payments begin immediately.

How to Calculate FV of Annuity Due (Example)

  1. Identify Components:

    An investor deposits $\mathbf{\$100\ (PMT)}$ at the beginning of every month for $\mathbf{12\ months\ (N)}$. The $\mathbf{Interest\ Rate\ (R)}$ is $0.5\%$ per month (6% annual rate).

  2. Apply the Formula:

    $$ FV = 100 \left[ \frac{(1+0.005)^{12} – 1}{0.005} \right] (1+0.005) $$

  3. Determine the FV:

    The Future Value is approximately $\mathbf{\$1,239.06}$. Note that the Future Value of an *ordinary* annuity in this scenario would be $\mathbf{\$1,233.56}$, demonstrating the benefit of paying at the period’s start.

  4. Verify Total Interest:

    Total payments made are $\$100 \times 12 = \$1,200$. The interest earned is $\$1,239.06 – \$1,200 = \mathbf{\$39.06}$.

Frequently Asked Questions (FAQ)

Q: What is the main difference between Annuity Due and Ordinary Annuity?

A: The only difference is the timing of the payment. Annuity Due payments occur at the beginning of the period, while Ordinary Annuity payments occur at the end. Annuity Due always results in a higher Future Value due to one extra compounding period of interest.

Q: Which formula should I use for a monthly mortgage payment?

A: Mortgage payments are typically made at the *end* of the period, so you should use the **Present Value of Ordinary Annuity** formula when calculating the monthly payment amount.

Q: Why does the Interest Rate ($R$) need to match the Number of Periods ($N$)?

A: For accurate calculation, the rate must be the rate per compounding period. If $N$ is in months (monthly payments), $R$ must be the monthly interest rate (Annual Percentage Rate / 12).

Q: Can I solve for the Interest Rate ($R$) directly?

A: No. The formula is structured such that $R$ must be solved using iterative numerical methods (like the Bisection Method or Newton’s Method), which is handled automatically by the solver logic in the calculator.

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