Savings Account Lump Sum

Compound Interest Formula:

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

Principal Amount (P):

Annual Interest Rate (r):

decimal

Compounding Periods per Year (n):

Time (t):

years

Future Value (FV):

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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:

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

Where:

\( FV \) — Future value of the investment
\( P \) — Principal investment amount
\( r \) — Annual interest rate (in decimal form)
\( n \) — Number of times interest is compounded per year
\( t \) — Time the money is invested for (in years)

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

3. Importance of Compound Interest

Details: Compound interest is a powerful concept in finance that allows investments to grow exponentially over time. It's the foundation of long-term savings and retirement planning, demonstrating the value of starting to invest early.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between compound and simple interest?
A: Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any accumulated interest.

Q2: How does compounding frequency affect returns?
A: The more frequently interest is compounded, the higher the effective return will be, as interest is earned on interest more often.

Q3: What is the Rule of 72?
A: The Rule of 72 is a simple way to estimate how long an investment will take to double: divide 72 by the annual interest rate.

Q4: Can this calculator be used for loans?
A: Yes, the same formula applies to compound interest on loans, though the future value would represent the total amount owed.

Q5: What is APY and how does it relate?
A: APY (Annual Percentage Yield) is the effective annual rate of return taking into account the effect of compounding interest.