Compound Interest Calculator Periodic Investment

Compound Interest Formula:

\[ A = PMT \times \frac{(1 + r)^m - 1}{r} \]

Periodic Investment (PMT):

currency units

Periodic Rate (r):

decimal

Number of Periods (m):

unitless

Future Value (A):

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1. What is the Compound Interest Formula?

The compound interest formula with periodic investment calculates the future value of regular investments that earn compound interest over time. It shows how money grows through regular contributions and the power of compounding returns.

2. How Does the Calculator Work?

The calculator uses the compound interest formula:

\[ A = PMT \times \frac{(1 + r)^m - 1}{r} \]

Where:

\( A \) — Future value (currency units)
\( PMT \) — Periodic investment amount (currency units)
\( r \) — Periodic interest rate (decimal)
\( m \) — Number of periods (unitless)

Explanation: The formula calculates the accumulated value of regular investments that earn compound interest at a specified rate over multiple periods.

3. Importance of Compound Interest Calculation

Details: Understanding compound growth is essential for financial planning, retirement savings, investment strategies, and achieving long-term financial goals through regular contributions.

4. Using the Calculator

Tips: Enter the periodic investment amount in currency units, the periodic interest rate as a decimal (e.g., 0.05 for 5%), and the number of periods. All values must be valid (investment > 0, rate ≥ 0, periods ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between simple and compound interest?
A: Simple interest is calculated only on the principal amount, while compound interest is calculated on both principal and accumulated interest, leading to exponential growth.

Q2: How often should I make periodic investments?
A: The frequency depends on your financial goals and cash flow. Common periods include monthly, quarterly, or annually, with more frequent investments generally yielding better results due to compounding.

Q3: What if the interest rate is zero?
A: When the interest rate is zero, the formula simplifies to A = PMT × m, meaning you simply accumulate the total of all your periodic investments without any interest earnings.

Q4: How does compounding frequency affect results?
A: More frequent compounding (e.g., monthly vs. annually) typically yields higher returns because interest is calculated and added to the principal more often, leading to faster growth.

Q5: Can this formula be used for different time periods?
A: Yes, but you must ensure consistency between the interest rate period and the investment period. For example, use monthly rate for monthly investments, or convert annual rates to equivalent periodic rates.