Savings Account Calculator

Compound Interest Formula:

\[ A = P \times \left(1 + \frac{r}{n}\right)^{n \times t} \]

Principal Amount (P):

Annual Interest Rate (r):

Time (t):

years

Compounding Frequency (n):

Final Amount (A):

Interest Earned:

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1. What is Compound Interest?

Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods. It's often called "interest on interest" and makes a sum grow at a faster rate than simple interest, which is calculated only on the principal amount.

2. How the Calculator Works

The calculator uses the compound interest formula:

\[ A = P \times \left(1 + \frac{r}{n}\right)^{n \times t} \]

Where:

$ A $ — Final amount ($)
$ P $ — Principal investment amount ($)
$ r $ — Annual interest rate (decimal)
$ n $ — Number of times interest is compounded per year
$ t $ — Time the money is invested for (years)

Explanation: The formula accounts for periodic compounding where interest is added to the principal at regular intervals, resulting in exponential growth.

3. Importance of Compounding Frequency

Details: The more frequently interest is compounded, the greater the return. Daily compounding yields more than monthly, which yields more than annual compounding, given the same annual rate and time period.

4. Using the Calculator

Tips: Enter the principal amount in dollars, annual interest rate as a percentage (e.g., 5 for 5%), time in years, and select how often interest is compounded. All values must be positive 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 the principal plus accumulated interest.

Q2: How does compounding frequency affect returns?
A: More frequent compounding leads to higher returns. For example, $10,000 at 5% compounded daily yields more than the same amount compounded annually over the same period.

Q3: What's the "Rule of 72"?
A: It's a quick way to estimate how long it takes to double your money: divide 72 by the interest rate. At 6%, it takes about 12 years (72/6 = 12).

Q4: Are there limitations to this calculation?
A: This assumes a fixed interest rate, no additional deposits or withdrawals, and doesn't account for taxes or inflation.

Q5: How can I maximize compound interest?
A: Start early (time is the most powerful factor), choose accounts with higher rates and more frequent compounding, and reinvest all earnings.