Future Value of Annuity Due Calculator

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Reviewed by: Dr. Sarah Chen, Financial Planning Expert, CFP®
Dr. Chen holds a Ph.D. in Finance and advises on retirement and complex time-value-of-money calculations.

The **Future Value of Annuity Due Calculator** determines the total value of a series of equal payments made at the **beginning** of each period, earning compound interest. This calculator allows you to solve for any missing variable: the **Future Value (FV)**, the **Periodic Payment (PMT)**, the **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 calculation is based on the Future Value of an Ordinary Annuity (FVOA) formula, modified by multiplying by $(1+i)$ to account for payments made at the start of the period.

$$ FV (F) = PMT (P) \times \left[ \frac{(1+i)^n – 1}{i} \right] \times (1+i) $$ $$ PMT (P) = \frac{FV (F) \times i}{((1+i)^n – 1) \times (1+i)} $$

Where $i = \frac{R}{100}$ (Interest Rate per Period) and $n = N$ (Number of Periods).

Formula Source: Investopedia: Future Value of an Annuity Due

Variables Explained

The key components of the FVAD calculation are:

  • Future Value (FV, F): The total accumulated value of the annuity at the end of the term ($).
  • Periodic Payment (PMT, P): The fixed amount paid at the beginning of each period ($).
  • Annual Interest Rate (R, V): The annual rate of return or discount rate (%). This is assumed to be compounded annually for simplicity in this model.
  • Number of Periods (N, Q): The total number of periods over which payments are made (Years).

Related Calculators

Compare and contrast other Time Value of Money (TVM) concepts:

What is the Future Value of an Annuity Due (FVAD)?

An **Annuity Due** is a series of payments made at the *beginning* of each period, such as rent payments, insurance premiums, or scheduled investment contributions (like a retirement plan deposit made on January 1st). The **Future Value of Annuity Due (FVAD)** calculates the total accumulated sum of these payments, including all earned interest, as of the end of the final period.

Because payments are made at the start of the period, each payment earns one extra period of compounding interest compared to an ordinary annuity. This difference results in a higher future value for an annuity due, all else being equal.

How to Calculate FVAD (Example)

  1. Identify Components:

    We want to find the Future Value ($FV$). Periodic Payment ($\mathbf{PMT}$) is $\mathbf{\$500}$. Annual Rate ($\mathbf{R}$) is $\mathbf{6\%}$. Number of Periods ($\mathbf{N}$) is $\mathbf{4}$ years.

  2. Convert Rate to Decimal (i):

    $$ i = \frac{6\%}{100} = \mathbf{0.06} $$

  3. Calculate the FVOA Factor:

    $$ FVOA factor = \frac{(1+0.06)^4 – 1}{0.06} \approx \mathbf{4.3746} $$

  4. Apply the Annuity Due Adjustment:

    $$ FVAD Factor = FVOA factor \times (1+i) = 4.3746 \times 1.06 \approx \mathbf{4.6371} $$

  5. Determine the Future Value (FV):

    $$ FV = PMT \times FVAD Factor = \$500 \times 4.6371 \approx \mathbf{\$2,318.55} $$ The estimated future value is $\mathbf{\$2,318.55}$.

Frequently Asked Questions (FAQ)

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

A: The difference lies in the timing of payments. Annuity Due payments are made at the **beginning** of the period, while Ordinary Annuity payments are made at the **end**. This difference results in a higher FV for the Annuity Due because it earns interest for one extra period.

Q: Is this calculator used for monthly payments?

A: This simplified model assumes annual payments and compounding. For monthly payments, you would typically adjust the rate ($i$) by dividing the annual rate by 12, and the periods ($n$) by multiplying the years by 12.

Q: Why is the FVAD value higher than FVOA?

A: The earlier payment allows the initial sum to compound for an additional period, resulting in a slightly higher final future value compared to an ordinary annuity.

Q: What is the purpose of knowing the FVAD?

A: It is primarily used in retirement planning, lease payment valuation, and insurance calculations to project how much a regular savings or investment plan will be worth at a future date.

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