Compound Calculator With Withdrawals

Compound Interest With Withdrawals Formula:

\[ FV = P \times (1 + r)^k + PMT \times \frac{(1 + r)^k - 1}{r} \]

Initial Amount (P):

currency units

Rate Per Period (r):

decimal

Number Of Periods (k):

unitless

Withdrawal Amount Per Period (PMT):

currency units (negative)

Future Value (FV):

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1. What is the Compound Interest With Withdrawals Formula?

The compound interest with withdrawals formula calculates the future value of an investment when regular withdrawals are made. It accounts for both the compounding growth of the initial investment and the impact of periodic withdrawals on the final value.

2. How Does the Calculator Work?

The calculator uses the compound interest with withdrawals formula:

\[ FV = P \times (1 + r)^k + PMT \times \frac{(1 + r)^k - 1}{r} \]

Where:

\( FV \) — Future value (currency units)
\( P \) — Initial amount (currency units)
\( r \) — Rate per period (decimal)
\( k \) — Number of periods (unitless)
\( PMT \) — Withdrawal amount per period (currency units, negative)

Explanation: The formula calculates the compounded growth of the initial investment and subtracts the compounded value of the withdrawals made during the investment period.

3. Importance of Future Value Calculation

Details: Calculating future value with withdrawals is essential for retirement planning, investment analysis, and understanding how regular withdrawals impact the growth of an investment portfolio over time.

4. Using the Calculator

Tips: Enter the initial investment amount, interest rate per period (as decimal), number of periods, and withdrawal amount (as negative value). All values must be valid (positive amounts where appropriate).

5. Frequently Asked Questions (FAQ)

Q1: Why is the withdrawal amount entered as negative?
A: The withdrawal is treated as a negative cash flow (money leaving the investment), which is why it's entered as a negative value in the calculation.

Q2: What time periods can be used?
A: The formula works for any consistent time period (months, quarters, years) as long as the rate matches the period (monthly rate for monthly periods, etc.).

Q3: How does this differ from regular compound interest?
A: Regular compound interest only considers growth of the initial investment, while this formula accounts for both growth and the impact of regular withdrawals.

Q4: Can this be used for deposits instead of withdrawals?
A: Yes, by entering positive values for PMT, the formula can calculate future value with regular deposits instead of withdrawals.

Q5: What if the withdrawal amount exceeds investment growth?
A: The formula will calculate a negative future value, indicating that the withdrawals have depleted the investment principal over time.