Compound Interest Calculator

Compound Interest Formula:

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

Principal Amount (P):

Annual Interest Rate (r):

unitless

Compounding Frequency (n):

unitless

Time Period (t):

years

Final Amount (A):

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1. What is Compound Interest?

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. It's often referred to as "interest on interest" and makes a sum grow at a faster rate than simple interest.

2. How Does the Calculator Work?

The calculator uses the compound interest formula:

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

Where:

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

Explanation: The formula calculates how much an investment will grow over time when interest is compounded at regular intervals.

3. Importance of Compound Interest Calculation

Details: Understanding compound interest is crucial for financial planning, investment decisions, and loan management. It demonstrates how investments can grow exponentially over time and how debt can accumulate if not properly managed.

4. Using the Calculator

Tips: Enter the principal amount in dollars, annual interest rate as a decimal (e.g., 0.05 for 5%), compounding frequency (how many times per year interest is compounded), and time period in years. 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 both the principal and accumulated interest.

Q2: How does compounding frequency affect the final amount?
A: The more frequently interest is compounded, the higher the final amount will be, as interest is calculated on a growing balance more often.

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

Q4: Can this calculator be used for loans as well as investments?
A: Yes, the same formula applies to both investments (where money grows) and loans (where debt accumulates).

Q5: What is the Rule of 72?
A: The Rule of 72 is a quick way to estimate how long it takes for an investment to double: divide 72 by the annual interest rate.