Financial theorist and investment analyst specializing in future cash flow modeling and retirement savings.
The **Future Value of Annuity Calculator** determines the total value of a series of regular payments, compounded over a period of time. This is critical for planning retirement savings, college funds, and calculating the final payoff of an investment. Enter any three variables (Future Payment, Future Value, Rate, or Term) to solve for the missing one.
Future Value of Annuity Calculator
Future Value of Annuity Formula Variations
The core formula assumes an Ordinary Annuity (payments made at the end of the period):
Let $M$ = Monthly Payment, $i$ = Monthly Rate ($R/1200$), and $N$ = Total Periods (Months).
Formula Source: Investopedia – Future Value of Annuity
Solving for each variable:
FV (P) = M × [ (1 + i)ᴺ - 1 ] ÷ i
M (F) = FV × i ÷ [ (1 + i)ᴺ - 1 ]
N (Q) = ln( 1 + FV × i ÷ M ) ÷ ln(1 + i)
R (V): Requires iteration (complex)
Variables Explained
- F (Future Payment Amount – M): The fixed cash flow amount contributed each period (e.g., monthly deposit).
- P (Future Value – FV): The accumulated value of the payments and compounded interest at the end of the term.
- V (Annual Compounding Rate – R): The yearly interest rate or expected rate of return on the investment.
- Q (Total Periods – N): The total number of contributions made over the annuity term (usually months).
Related Calculators
- Compound Interest Savings Calculator
- Retirement Goal Calculator
- Present Value of Annuity Calculator
- Required Contribution Calculator
What is the Future Value of Annuity?
The **Future Value of Annuity (FVA)** is the accumulated total amount, including both the principal contributions and the compounded interest, that a series of equal payments will be worth at a specified future date. This is an essential calculation for anyone planning long-term savings or investments, such as retirement accounts or educational funds.
Unlike simple savings where interest is calculated only on the principal, FVA accounts for the fact that each payment earns interest on itself and the accumulated interest from previous periods. The higher the compounding rate ($R$) and the longer the period ($N$), the greater the impact of compounding on the final future value.
How to Calculate FVA (Example)
Scenario: You deposit $500 per month for 10 years (120 months) into an account earning 7% annually, compounded monthly.
- Determine the Monthly Rate (i):
$$i = 7\% \div 12 \approx 0.5833\% \text{ or } 0.005833$$
- Calculate the Growth Factor:
$$ \frac{(1 + 0.005833)^{120} – 1}{0.005833} \approx 173.085$$
- Apply the Formula (Solve for FV):
$$FV = \$500 \times 173.085 \approx \$86,542.50$$
- Final Result:
The future value of the $500/month stream after 10 years is approximately $86,542.50.
Frequently Asked Questions (FAQ)
The simple sum of deposits would be $500 \times 120 = \$60,000$. The difference between the FVA ($86,542.50) and the simple sum ($60,000) is the total compounded interest earned ($26,542.50).
Does the calculator assume monthly compounding?Yes, since the payment frequency is in months, the calculation assumes the annual rate is divided by 12 and compounded 12 times per year.
How does FVA relate to retirement planning?FVA is the primary tool used in defined contribution retirement plans (like 401k or IRA) to project the total wealth accumulated by the time the saver reaches their retirement goal date.
Can I solve for the required Future Payment (M)?Yes, by rearranging the FVA formula, you can find the monthly contribution required to reach a specific future savings goal (Future Value).