How is compound interest calculated when it's compounded more frequently than annually

Questions : How is compound interest calculated when it's compounded more frequently than annually?

Answer:  

 Use the formula:

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

where:

• $P$ is the principal amount,
• $r$ is the annual interest rate,
• $n$ is the number of times interest is compounded per year,
• $t$ is the time in years.

Additional Information

Let's break down how to calculate compound interest. It's a powerful concept where you earn interest not only on your initial principal but also on the accumulated interest from previous periods.¹

Understanding the Terms

• Principal (P): The initial amount of money you invest or borrow.²
• Interest Rate (r): The annual percentage rate (APR) expressed as a decimal (e.g., 5% = 0.05).
• Number of Times Interest is Compounded per Year (n): How often the interest is calculated and added to the principal (e.g., annually, quarterly, monthly, daily).³
• Time (t): The number of years the money is invested or borrowed for.⁴
• Future Value (A): The total amount you'll have after the time period, including both the principal and the accumulated interest.

The Formula

The formula for compound interest is:

A = P (1 + r/n)^(nt)⁵

Let's Walk Through an Example

Suppose you invest $1,000 (P) at an annual interest rate of 6% (r = 0.06), compounded quarterly (n = 4), for 5 years (t).

1. Plug in the values:

   A = 1000 (1 + 0.06/4)^(4*5)

2. Simplify inside the parentheses:

   A = 1000 (1 + 0.015)^(20)

3. Calculate the part in the parentheses:

   A = 1000 (1.015)^(20)

4. Raise 1.015 to the power of 20:

   A = 1000 (1.346855) (approximately)

5. Multiply by the principal:

   A = $1346.86 (approximately)

So, after 5 years, you would have approximately $1346.86 in your account.

Key Points

• The more frequently interest is compounded, the faster your money grows.⁶ Daily compounding will result in slightly more interest than quarterly compounding, which will be more than annual compounding, and so on.⁷
• Compound interest can work for you (investing) or against you (loans). It's a powerful force!⁸

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