Open Saving Account The Plan And Goal

Compound Interest Formula:

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

Initial Principal (P):

Annual Interest Rate (r):

decimal

Compounding Periods Per Year (n):

Time (t):

years

Periodic Payment (PMT):

$ per period

Future Value (FV):

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1. What Is The Compound Interest Formula?

The compound interest formula calculates the future value of an investment or savings account, taking into account both the initial principal and periodic contributions, with interest compounded at regular intervals.

2. How Does The Calculator Work?

The calculator uses the compound interest formula:

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

Where:

$ FV $ — Future value ($)
$ P $ — Initial principal ($)
$ r $ — Annual interest rate (decimal)
$ n $ — Number of compounding periods per year
$ t $ — Time in years
$ PMT $ — Periodic payment ($ per period)

Explanation: The formula calculates how much your investment will grow over time with compound interest and regular contributions.

3. Importance Of Future Value Calculation

Details: Calculating future value helps in financial planning, setting savings goals, and understanding how compound interest can grow your investments over time.

4. Using The Calculator

Tips: Enter all values in the specified units. Ensure the interest rate is in decimal form (e.g., 5% = 0.05). All values must be non-negative.

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 the principal and accumulated interest.

Q2: How does compounding frequency affect returns?
A: More frequent compounding (higher n) results in higher returns due to interest being calculated more often.

Q3: Can this calculator handle irregular contributions?
A: No, this calculator assumes regular, consistent periodic payments. For irregular contributions, more complex calculations are needed.

Q4: What if I don't make periodic payments?
A: Set PMT to 0 to calculate future value based only on the initial principal with compound interest.

Q5: How accurate is this calculation for real-world investments?
A: This provides a mathematical estimate. Actual returns may vary due to changing interest rates, fees, and other factors.