Digit Money Saving Review

Compound Interest Formula:

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

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 that earns interest on both the initial principal and the accumulated interest from previous periods, including regular contributions.

2. How Does the Calculator Work?

The calculator uses the compound interest formula with regular contributions:

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

Where:

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

Explanation: The formula accounts for compound growth of both the initial investment and regular contributions made at each compounding period.

3. Importance of Future Value Calculation

Details: Calculating future value helps in financial planning, retirement savings estimation, investment comparison, and understanding the power of compound interest over time.

4. Using the Calculator

Tips: Enter initial principal in dollars, annual interest rate as a decimal (e.g., 0.05 for 5%), number of compounding periods per year, time in years, and periodic payment amount. All values must be valid non-negative numbers.

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 and added more often.

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

Q4: Can I use this for retirement planning?
A: Yes, this calculator is useful for estimating retirement savings growth with regular contributions.

Q5: What if the interest rate is zero?
A: The formula simplifies to FV = P + (PMT × n × t), calculating simple accumulation without interest.