This Future Value of Annuity Calculator is based on the standard monthly compounding annuity formula, which is crucial for accurate retirement and savings planning. The calculations are verified against established financial models.
Welcome to the **Future Value of Annuity Calculator**. An annuity represents a series of equal payments made at regular intervals (like monthly retirement contributions). This tool helps you solve for any missing variable—the Future Value (FV), the required Payment (PMT), the Annual Rate (r), or the Time (t)—by providing the other three inputs. Start planning your long-term savings goals today!
Future Value of Annuity Calculator
Future Value of Annuity Formula
The core formula for Future Value of an Ordinary Annuity (FV) is:
FV = PMT × [ (1 + i)n – 1 / i ]
Where i is the monthly rate (r/12) and n is the total number of periods (t × 12).
1. Solve for Future Value (FV):
FV = PMT × [ ( (1 + i)n – 1 ) / i ]
2. Solve for Periodic Payment (PMT):
PMT = FV × [ i / ( (1 + i)n – 1 ) ]
3. Solve for Time in Years (t):
t = ln( (FV × i / PMT) + 1 ) / (12 × ln(1 + i))
4. Solve for Annual Rate (r):
r = Iterative Numerical Approximation (e.g., Bisection Method)
Formula Source: Investopedia – Future Value of Annuity
Variables Explained
- FV – Future Value: The total accumulated value of all payments plus compounded interest at the end of the term.
- PMT – Periodic Payment: The fixed amount of money paid or contributed at the end of each period (assumed monthly).
- r – Annual Interest Rate: The annual nominal rate of return (expressed as a decimal, e.g., 0.07).
- t – Time in Years: The total length of the investment in years.
- i – Periodic Rate: The monthly interest rate (r / 12).
- n – Number of Periods: The total number of payments (t × 12).
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What is Future Value of Annuity?
The Future Value of an Annuity (FVA) is a financial metric used to determine how much a series of equal, periodic payments will be worth at a specific date in the future, assuming a constant interest rate. This concept is fundamental to retirement planning, college funds, and other systematic savings goals.
The value grows due to two factors: the sum of the regular payments (the principal contributions) and the compounded interest earned on both the payments and the interest accrued in previous periods. The calculation assumes an “ordinary annuity,” where payments are made at the end of each period.
By using the FVA, investors can project their total wealth accumulation over a fixed period, which is essential for determining the feasibility of achieving long-term financial objectives. It helps establish the necessary payment size or investment term required to reach a target savings amount.
How to Calculate Future Value (Example)
Let’s calculate the Future Value (FV) of a $100 monthly contribution (PMT=$100) for 10 years (t=10) at a 5% annual rate (r=0.05):
- Determine Periods (n) and Monthly Rate (i): $n = 10 \times 12 = 120$ periods. $i = 0.05 / 12 \approx 0.004167$.
- Calculate the Growth Factor: $(1 + i)^n = (1.004167)^{120} \approx 1.647009$.
- Calculate the Annuity Factor: $\frac{(1 + i)^n – 1}{i} = \frac{1.647009 – 1}{0.004167} \approx 155.334$.
- Determine the Future Value (FV): $FV = PMT \times \text{Factor} = \$100 \times 155.334 \approx \$15,533.40$.
Frequently Asked Questions (FAQ)
An Ordinary Annuity assumes payments are made at the *end* of each period (used here). An Annuity Due assumes payments are made at the *beginning*, resulting in a slightly higher FV because each payment earns interest for one extra period.
Can the Future Value of Annuity formula be used for retirement savings?Yes, it is the standard formula for estimating the size of a retirement fund, provided the contributions are fixed and regular, and the expected rate of return is consistent.
How does inflation affect the Future Value of Annuity?The calculated FV is a nominal value. Inflation erodes purchasing power. To get the ‘real’ FV, you should use the inflation-adjusted (real) rate of return for ‘r’ in the calculation.
Why is solving for the Interest Rate (r) difficult in this formula?Similar to loan amortization, the interest rate is trapped inside exponential and fractional terms. It cannot be isolated algebraically and requires numerical methods to approximate the correct value.