Accumulated Future Value Calculator

Future Value Formula:

\[ FV = PV \times (1 + r)^t + PMT \times \left(\frac{(1 + r)^t - 1}{r}\right) \]

Present Value (PV):

USD

Interest Rate (r):

decimal

Time Period (t):

years

Periodic Payment (PMT):

USD

Future Value (FV):

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1. What is the Future Value Calculation?

The Future Value calculation determines how much an investment or series of payments will grow to at a future date, given a specified interest rate. It accounts for both lump sum investments (PV) and periodic contributions (PMT).

2. How Does the Calculator Work?

The calculator uses the Future Value formula:

\[ FV = PV \times (1 + r)^t + PMT \times \left(\frac{(1 + r)^t - 1}{r}\right) \]

Where:

\( PV \) — Present value or initial investment (USD)
\( r \) — Periodic interest rate (decimal)
\( t \) — Number of periods (years)
\( PMT \) — Periodic payment (USD)

Explanation: The first part calculates growth of the initial investment, while the second part calculates the accumulated value of periodic payments.

3. Importance of Future Value Calculation

Details: Future Value calculations are essential for financial planning, retirement savings projections, investment analysis, and loan amortization.

4. Using the Calculator

Tips: Enter present value in USD, interest rate as decimal (e.g., 0.05 for 5%), time in years, and periodic payment in USD. All values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between FV and PV?
A: PV is the current value, while FV is what that value will grow to in the future with compound interest.

Q2: How does compounding frequency affect results?
A: This calculator assumes annual compounding. For different compounding periods, adjust the rate and time accordingly.

Q3: What if my periodic payment is 0?
A: The formula simplifies to just the growth of your initial investment (PV × (1 + r)^t).

Q4: What if my interest rate is 0%?
A: The formula simplifies to PV + (PMT × t) - just the sum of all contributions.

Q5: Can I use this for monthly calculations?
A: Yes, but convert annual rate to monthly (divide by 12) and time to months (multiply by 12).