Savings in Common Goals

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 by accounting for both the initial principal and the interest earned on previously accumulated interest. It's essential for planning long-term financial goals.

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 combines the growth of the initial investment with the accumulated value of regular contributions, accounting for compound interest over time.

3. Importance of Future Value Calculation

Details: Calculating future value helps individuals plan for financial goals such as retirement, education funds, or major purchases by showing how savings can grow over time with compound interest.

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 with n > 0.

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

Q3: What are typical compounding periods?
A: Common periods include annually (n=1), semi-annually (n=2), quarterly (n=4), monthly (n=12), and daily (n=365).

Q4: Can this calculator handle irregular payments?
A: No, this calculator assumes regular, consistent periodic payments. For irregular payments, more complex calculations are needed.

Q5: Is this suitable for all types of investments?
A: This formula works best for fixed-rate investments. Variable rate investments or those with fees may require different calculations.