Dr. Vance holds a Ph.D. in Financial Economics and specializes in Time Value of Money (TVM) applications for retirement planning.
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, earning compound interest. This versatile 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 Ordinary Annuity Calculator
Future Value of Ordinary Annuity Formulas
The core FVOA formula is the foundation of many long-term financial projections, especially for retirement savings. It calculates the value of the payments compounded over time:
Where $i = \frac{R}{100}$ (Interest Rate per Period, decimal) and $n = N$ (Number of Periods, years).
Formula Source: Investopedia: Future Value of an Ordinary Annuity
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 stream of equal, fixed payments made at the **end** of each period. Examples include regular bond coupon payments or mortgage interest payments. The **Future Value of Ordinary Annuity (FVOA)** is the total cash sum the investor or saver would have accumulated, including all earned interest, by the time the last payment is made.
The concept is foundational in finance and retirement planning. Because payments are made at the end of the period, they do not earn interest during that specific period. This differs from an annuity due, where payments are made at the beginning, leading to one extra period of compounding interest.
How to Calculate FVOA (Example)
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Identify Components:
We want to find the Future Value ($FV$). Periodic Payment ($\mathbf{PMT}$) is $\mathbf{\$750}$. Annual Rate ($\mathbf{R}$) is $\mathbf{7\%}$. Number of Periods ($\mathbf{N}$) is $\mathbf{18}$ years.
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Convert Rate to Decimal (i) and Periods (n):
$$ i = \frac{7\%}{100} = \mathbf{0.07} $$ and $n=18$.
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Calculate the FVOA Factor:
$$ FVOA factor = \frac{(1+0.07)^{18} – 1}{0.07} \approx \mathbf{34.8054} $$
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Determine the Future Value (FV):
$$ FV = PMT \times FVOA Factor = \$750 \times 34.8054 \approx \mathbf{\$26,104.05} $$ The estimated future value is $\mathbf{\$26,104.05}$.
Frequently Asked Questions (FAQ)
A: The convention of the ordinary annuity is that the payment is received or made at the closing of the period. This contrasts with an annuity due, where the transaction occurs at the beginning of the period.
A: Higher compounding frequency (e.g., monthly) leads to a higher FV. However, this model assumes annual compounding. For monthly accuracy, the inputs must be adjusted: $i_{monthly} = R / 12$ and $n_{monthly} = N \times 12$.
A: Yes. While FVOA calculates future value, the underlying time value of money factor is used in reverse (Present Value of Annuity) to calculate loan principal and mortgage payments.
A: If $R=0$, the FVOA simplifies to just the total payments made: $FV = PMT \times N$. Our JavaScript logic handles this case separately to avoid division by zero.