https://file.aiquickdraw.com/mathbot/file/17282612081342502mqdc.jpg

To solve the problem from the image, we need to determine two things:
1. The **total number of compounding periods**.
2. The **interest rate per compounding period**.

### Given Data:
- **Term of Investment**: 8 years
- **Nominal (Annual) Rate**: 4%
- **Interest Compounded**: Quarterly

### Step 1: Finding the Total Number of Compounding Periods

When interest is compounded quarterly, this means that interest is compounded 4 times per year. So, for the total number of compounding periods, we multiply the number of years by the number of compounding periods per year.

\[
\text{Total Compounding Periods} = \text{Years} \times \text{Compounding Periods per Year}
\]

\[
= 8 \times 4 = 32 \text{ periods}
\]

### Step 2: Finding the Interest Rate per Compounding Period

Since the interest is compounded quarterly, we need to divide the annual nominal interest rate by the number of periods per year to get the rate per period.

\[
\text{Rate per Period} = \frac{\text{Nominal Annual Rate}}{\text{Compounding Periods per Year}}
\]

\[
= \frac{4\%}{4} = 1\%
\]

### Final Answers:
- **Compounding Periods**: 32 periods
- **Rate per Period**: 1%

Would you like more details on any part of the solution?

Here are 5 related questions to extend this topic:
1. What happens to the number of periods if the compounding is done monthly?
2. How does a change in the nominal rate affect the rate per period?
3. Can you explain how continuous compounding differs from quarterly compounding?
4. What is the formula for finding the future value of an investment using compound interest?
5. How would the total number of periods change for an investment term of 10 years?

**Tip**: Compounding more frequently (like monthly or daily) leads to a higher effective interest rate, even if the nominal rate stays the same!

Find the total number of compounding periods and the interest rate per period for the investment.

Learn how to calculate the total compounding periods and interest rate per period for an 8-year investment with a 4% nominal annual rate compounded quarterly. Understand the formulas and steps for determining compounding periods and rate per period.

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