A bank advertises that it pays interest on saving accounts at the rate of 4.25% compounded daily. Find the effective rate if the bank uses 360days in determining the daily rate. Round the answer to three decimal places.




To find the effective annual rate (EAR) given a nominal interest rate of 4.25% compounded daily with 360 days per year, you can use the following formula for effective interest rate:

\[
\text{Effective Rate} = \left(1 + \frac{r}{n}\right)^n - 1
\]

Where:
- \( r \) is the nominal annual interest rate (4.25% or 0.0425),
- \( n \) is the number of compounding periods per year (360 days).

Let's plug the values into the formula:

\[
\text{Effective Rate} = \left(1 + \frac{0.0425}{360}\right)^{360} - 1
\]

Now, I'll compute that.The effective annual rate (EAR) is approximately **4.3%** when the interest is compounded daily, using 360 days per year.

Would you like more details or have any questions? Here are 5 related questions to explore:

1. What is the difference between nominal and effective interest rates?
2. How does daily compounding affect savings growth compared to monthly compounding?
3. What happens if the bank uses 365 days instead of 360 days for compounding?
4. How would the effective rate change if the nominal rate was increased to 5%?
5. Can you explain the formula used for calculating effective interest rates?

**Tip:** The more frequently interest is compounded, the higher the effective rate compared to the nominal rate!

A bank advertises that it pays interest on saving accounts at the rate of 4.25% compounded daily. Find the effective rate if the bank uses 360 days in determining the daily rate. Round the answer to three decimal places.

Learn how to calculate the effective interest rate for a nominal rate of 4.25% compounded daily using 360 days per year. This detailed solution covers key concepts such as interest compounding and exponential growth, making it suitable for high school students in Grades 10-12.

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