Your bank account pays interest with an EAR of 6%. What is the APR quote for this account based on semiannual​ compounding? What is the APR with monthly​ compounding?

To find the **APR (Annual Percentage Rate)** based on different compounding periods, we can use the formula that relates the **EAR (Effective Annual Rate)** to the APR for each compounding period.

The formula is:

\[
EAR = \left(1 + \frac{APR}{n}\right)^n - 1
\]

Where:
- \( EAR \) is the effective annual rate (6% or 0.06),
- \( APR \) is the annual percentage rate (which we are solving for),
- \( n \) is the number of compounding periods per year.

We need to solve for APR for both semiannual and monthly compounding.

### Step 1: APR with Semiannual Compounding
For **semiannual compounding**, \( n = 2 \).

\[
0.06 = \left(1 + \frac{APR_{semi}}{2}\right)^2 - 1
\]

Solving for \( APR_{semi} \).

### Step 2: APR with Monthly Compounding
For **monthly compounding**, \( n = 12 \).

\[
0.06 = \left(1 + \frac{APR_{monthly}}{12}\right)^{12} - 1
\]

Solving for \( APR_{monthly} \).

Let me compute these values for you.The APR (Annual Percentage Rate) based on the given EAR of 6% is:

1. **With semiannual compounding**: \( \approx 5.91\% \)
2. **With monthly compounding**: \( \approx 5.84\% \)

Would you like a detailed explanation or further clarification?

Here are 5 related questions to expand this topic:
1. How does the APR change with different compounding frequencies?
2. Can the EAR ever be lower than the APR?
3. What is the formula for APR when compounding is continuous?
4. How does APR affect the total interest paid over a loan term?
5. What are the practical implications of choosing monthly versus semiannual compounding?

**Tip**: The greater the number of compounding periods, the smaller the APR for a given EAR!

Your bank account pays interest with an EAR of 6%. What is the APR quote for this account based on semiannual compounding? What is the APR with monthly compounding?

Learn how to calculate the APR (Annual Percentage Rate) from an EAR (Effective Annual Rate) of 6% with semiannual and monthly compounding. Understand the formula EAR = (1 + APR/n)^n - 1 and explore key finance concepts like interest rates and compounding.

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