Investment specialist and expert in retirement planning and future value analysis.
The **Future Value of Ordinary Annuity Calculator** determines the total value (Future Value) of a series of equal, periodic deposits made at the end of each period, earning a compounded rate of return. Enter any three of the core parameters ($\text{FV}, \text{PMT}, R, N$) to solve for the missing one.
Future Value of Ordinary Annuity Calculator
Instructions: Enter values for exactly three of the four core parameters to solve for the missing one.
Annuity Parameters
FVOA Formula
The core relationship for Future Value of an Ordinary Annuity (payment at end of period):
$$FV = PMT \left[ \frac{(1 + R)^{N} – 1}{R} \right]$$ Formula Source: InvestopediaVariables Explained (Q, F, P, V – Parameters)
- $\text{PMT}$ (Periodic Payment, $Q$): The constant, recurring payment amount made at the end of each period.
- $\text{FV}$ (Future Value, $F$): The total accumulated value of the annuity at the end of the term.
- $R$ (Rate per Period, $P$): The interest rate per compounding period (e.g., annual rate / 12 for monthly).
- $N$ (Number of Periods, $V$): The total number of payments (e.g., years $\times$ 12 for monthly payments).
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What is Future Value of Ordinary Annuity?
The **Future Value of an Ordinary Annuity** (FVOA) is the accumulated worth of a series of equal, fixed payments or deposits when those payments are made at the end of each compounding period. The final value includes both the sum of all payments made and the total compounded interest earned over the investment term.
This is the standard calculation used for retirement savings, education funds, and any systematic savings plan where contributions are made regularly (e.g., monthly 401k contributions or annual IRA deposits). The FVOA assumes that the compounding frequency matches the payment frequency, which is necessary for accurate calculations.
How to Calculate FVOA (Example)
A saver deposits \$200 at the end of each month for 5 years ($N=60$). The account earns an annual interest rate of 8% (0.08), compounded monthly ($R=0.08/12 \approx 0.006667$).
- Step 1: Calculate the Annuity Factor
Calculate the growth factor for $N=60$ and $R=0.006667$: $$\frac{(1 + 0.006667)^{60} – 1}{0.006667} \approx \mathbf{73.4764}$$
- Step 2: Apply the Formula
$$FV = PMT \times \text{Annuity Factor}$$
- Step 3: Calculate the Result
$$FV = \$200 \times 73.4764 \approx \mathbf{\$14,695.28}$$
The Future Value of the ordinary annuity is $\mathbf{\$14,695.28}$.
Frequently Asked Questions (FAQ)
Ordinary Annuity assumes payments are made at the **end** of the period, meaning the final payment earns no interest. Annuity Due assumes payments are made at the **beginning** of the period, so every payment (including the final one) earns interest for the full period, resulting in a slightly higher Future Value.
Yes. If you know your target future value ($\text{FV}$), the rate, and the number of periods, the calculator can solve for the required periodic payment ($\text{PMT}$).
It means the annual interest rate must be divided by the number of times compounding occurs per year. For example, if you have an 8% annual rate compounded monthly, the rate per period ($R$) is $0.08 / 12 = 0.006667$.
For loans, the Present Value of Annuity formula is typically used. The Future Value formula is primarily used for accumulating savings or investments.