Your sister recently landed her dream job. As part of planning for future expenses, she started to deposit Php 1,000.00 monthly in a fund that pays 6% compounded quarterly. What is the equivalent interest?

To calculate the equivalent interest rate for a fund paying 6% interest compounded quarterly, we need to find the **effective annual rate (EAR)**. The EAR shows the equivalent interest rate if compounding happened annually, taking into account the effect of compounding at shorter intervals (in this case, quarterly).

We can use the formula for **EAR**:

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

Where:
- \( r \) is the nominal annual interest rate (6% or 0.06).
- \( n \) is the number of compounding periods per year (quarterly, so \( n = 4 \)).

Let's compute the EAR.The equivalent annual interest rate (effective annual rate, EAR) is approximately **6.14%**. This means that although the nominal interest rate is 6% compounded quarterly, the actual interest earned over a year is equivalent to earning 6.14% with annual compounding.

Would you like more details on this or have any questions?

Here are five related questions to further explore the topic:
1. How would the equivalent interest rate change if compounding were monthly instead of quarterly?
2. How can you calculate the future value of your sister's savings after a certain number of years?
3. What is the impact of increasing the deposit amount on the future value of the fund?
4. How does the frequency of compounding affect the overall returns in an investment?
5. How would the equivalent interest rate be affected by a higher nominal interest rate?

**Tip:** The more frequently interest is compounded, the higher the effective annual interest rate will be, even if the nominal rate remains the same.

Find out how to calculate the equivalent interest for a fund that pays 6% compounded quarterly. This problem uses the Effective Annual Rate (EAR) formula to show how compounding affects the real return rate. Perfect for students in Grades 10-12 or anyone interested in financial mathematics.

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