Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. Here’s a clear example:

Formula for Compound Interest:

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

Where:

• $A$ = Future Value (total amount)
• $P$ = Principal amount (initial investment)
• $r$ = Annual interest rate (in decimal form, e.g., 5% = 0.05)
• $n$ = Number of times interest is compounded per year
• $t$ = Time (in years)

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Example:

Suppose you invest $1,000 at an annual interest rate of 5% compounded monthly for 3 years.

Given:

• $P = 1000$
• $r = 0.05$
• $n = 12$ (monthly compounding)
• $t = 3$

Step 1: Plug into the formula

$A = 1000 \times \left(1 + \frac{0.05}{12}\right)^{12 \cdot 3}$

Step 2: Simplify the terms

$A = 1000 \times \left(1 + 0.0041667\right)^{36}$ $A = 1000 \times (1.0041667)^{36}$

Step 3: Calculate

$A = 1000 \times 1.1616$ $A = 1161.60$

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Final Answer:

After 3 years, the total amount will be $1,161.60. This includes $161.60 as interest earned.

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Do you want me to explain this further or calculate for different parameters?

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Related Questions:

1. What happens if the compounding frequency changes to yearly or daily?
2. How does compound interest differ from simple interest?
3. What is the impact of doubling the time or the rate of interest on the final amount?
4. Can compound interest be negative? How would that work?
5. How is compound interest used in real-world scenarios like loans or investments?

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Tip:

The more frequently the interest is compounded, the faster your money grows. Aim for frequent compounding to maximize