Compound interest is a powerful concept in finance where the interest earned on an initial principal amount also earns interest in subsequent periods. This leads to exponential growth of the loan or investment over time.

The compound interest formula is:

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

Where:

• $A$ = Future value (total amount including principal and interest)
• $P$ = Principal (initial loan or investment amount)
• $r$ = Annual interest rate (decimal form, e.g., 5% = 0.05)
• $n$ = Number of times the interest is compounded per year
• $t$ = Time the money is invested or borrowed for, in years

Example:

If you borrow $10,000 at an annual interest rate of 5% compounded yearly for 3 years:

• $P = 10,000$
• $r = 0.05$
• $n = 1$ (compounded yearly)
• $t = 3$

$A = 10,000 \left(1 + \frac{0.05}{1}\right)^{1 \cdot 3} = 10,000 \cdot (1.05)^3 = 10,000 \cdot 1.157625 = 11,576.25$

The total amount owed after 3 years is $11,576.25, with $1,576.25 being interest.

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Would you like to see further examples or details? Here are 5 related questions to expand your understanding:

1. What is the difference between compound interest and simple interest?
2. How does changing the compounding frequency (e.g., monthly vs yearly) affect the total amount?
3. Can compound interest work to your advantage in investments?
4. What happens if you repay part of the principal during the term?
5. How do continuous compounding calculations differ from standard compounding?

Tip: To reduce the effect of compound interest on loans, try to make extra payments on the principal whenever possible.