Compound Interest Calculator Formula

Compound Interest Formula:

\[ A = P \times \left(1 + \frac{R}{100 \times n}\right)^{n \times T} \]

Principal (P):

currency units

Annual Interest Rate (R):

Compounding Frequency (n):

Time (T):

years

Final Amount (A):

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1. What is the Compound Interest Formula?

The compound interest formula calculates the future value of an investment or loan where interest is added to the principal at regular intervals, allowing the interest to earn additional interest over time.

2. How Does the Calculator Work?

The calculator uses the compound interest formula:

\[ A = P \times \left(1 + \frac{R}{100 \times n}\right)^{n \times T} \]

Where:

\( A \) — Final amount (currency units)
\( P \) — Principal amount (currency units)
\( R \) — Annual interest rate (%)
\( n \) — Compounding frequency per year (unitless)
\( T \) — Time in years

Explanation: The formula accounts for the effect of compounding, where interest is calculated on both the initial principal and the accumulated interest from previous periods.

3. Importance of Compound Interest Calculation

Details: Understanding compound interest is crucial for financial planning, investment decisions, loan calculations, and retirement planning. It demonstrates how money can grow exponentially over time.

4. Using the Calculator

Tips: Enter the principal amount, annual interest rate, select compounding frequency, and time period. 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: More frequent compounding results in higher returns because interest is calculated and added to the principal more often.

Q3: What is the Rule of 72?
A: The Rule of 72 estimates how long it takes for an investment to double at a given interest rate (72 divided by the interest rate).

Q4: Can this calculator be used for loans?
A: Yes, the same formula applies to both investments and loans, though for loans it calculates the total amount to be repaid.

Q5: What is continuous compounding?
A: Continuous compounding uses the formula \( A = P \times e^{R \times T} \) where e is Euler's number (approximately 2.71828).