Dr. Reed holds a Ph.D. in Financial Mathematics and has authored several foundational textbooks on the Time Value of Money (TVM).
The **Future Value of Ordinary Annuity Calculator** determines the total accumulated value of a series of equal payments made at the **end** of each period, assuming compound interest. Use this calculator 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 Ordinary Annuity Calculator
Future Value of Ordinary Annuity Formulas
The core FVOA calculation uses the future value interest factor of an annuity (FVIFA) to determine the total accumulated amount:
Where $i = \frac{R}{100}$ (Interest Rate per Period, decimal) and $n = N$ (Number of Periods, years).
Formula Source: The Balance: Future Value of Ordinary Annuity Formula
Variables Explained
The key components of the FVOA calculation are:
- Future Value (FV, F): The total accumulated value of all payments plus compound interest at the end of the term ($).
- Periodic Payment (PMT, P): The fixed amount paid at the end of each period ($).
- Annual Interest Rate (R, V): The annual rate of return or discount rate (%). This assumes annual compounding for this specific model.
- Number of Periods (N, Q): The total number of periods over which payments are made (Years).
Related Calculators
Explore these essential Time Value of Money (TVM) concepts for better financial planning:
- Future Value of Annuity Due Calculator
- Future Value of Single Sum Calculator
- Present Value of Ordinary Annuity Calculator
- Compound Annual Growth Rate Calculator
What is the Future Value of an Ordinary Annuity (FVOA)?
An **Ordinary Annuity** is a series of equal, fixed payments made at the **end** of each period. This is the most common annuity type encountered in finance, typical of bond coupon payments or contributions to retirement accounts at year-end. The **Future Value (FV)** is the total accumulated sum of these contributions and all accrued compound interest up to the date of the last payment.
Since the payment occurs at the end of the period, it begins earning compound interest only from the start of the next period. This timing convention simplifies certain long-term planning scenarios, differentiating it from an annuity due.
How to Calculate FVOA (Example)
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Identify Components:
We want to find the Future Value ($FV$). Periodic Payment ($\mathbf{PMT}$) is $\mathbf{\$500}$. Annual Rate ($\mathbf{R}$) is $\mathbf{6.5\%}$. Number of Periods ($\mathbf{N}$) is $\mathbf{10}$ years.
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Convert Rate to Decimal (i) and Periods (n):
$$ i = \frac{6.5\%}{100} = \mathbf{0.065} $$ and $n=10$.
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Calculate the FVOA Factor (FVIFA):
$$ FVOA factor = \frac{(1+0.065)^{10} – 1}{0.065} \approx \mathbf{13.4866} $$
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Determine the Future Value (FV):
$$ FV = PMT \times FVOA Factor = \$500 \times 13.4866 \approx \mathbf{\$6,743.30} $$ The estimated future value is $\mathbf{\$6,743.30}$.
Frequently Asked Questions (FAQ)
A: The difference is the timing of the payment. Ordinary Annuity payments occur at the **end** of the period (which this calculator uses), while Annuity Due payments occur at the **beginning** of the period, resulting in one extra period of compounding interest.
A: While the loan term (N) is typically a whole number, this calculator’s underlying formula can handle fractional periods mathematically, which might occur in complex financial structures.
A: This specific simplified model assumes the compounding frequency matches the payment frequency (annual). For scenarios involving monthly payments and monthly compounding, the inputs for R and N should be adjusted (Rate/12, N*12).
A: It means if you know the outcome (FV), the required time (N), and the interest rate (R), the calculator can work backward to tell you the required regular contribution amount (PMT).