Determine m​, ​n, and i for money invested at 8​% compounded quarterly for 9.5 years.
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Part 1
mequals
  
enter your response here ​(Type an integer or a​ decimal.)
Part 2
nequals
  
enter your response here ​(Type an integer or a​ decimal.)
Part 3
iequals
  
enter your response here​% ​(Round to four decimal places as​ needed.)

To solve for \( m \), \( n \), and \( i \) when dealing with money invested at an interest rate compounded quarterly, we can use the following steps:

### Definitions:
1. **\( m \)**: Number of compounding periods per year.
2. **\( n \)**: Total number of compounding periods.
3. **\( i \)**: Interest rate per compounding period.

Given:
- Annual interest rate \( r = 8\% \).
- Compounding frequency: Quarterly (4 times a year).
- Time \( t = 9.5 \) years.

### Part 1: Find \( m \)
\( m \) is the number of compounding periods per year.

\[
m = 4
\]

### Part 2: Find \( n \)
\( n \) is the total number of compounding periods.

\[
n = m \times t = 4 \times 9.5 = 38
\]

### Part 3: Find \( i \)
\( i \) is the interest rate per compounding period.

\[
i = \frac{r}{m} = \frac{8\%}{4} = 2\% \text{ per period}
\]

Expressing \( i \) as a decimal:

\[
i = \frac{2}{100} = 0.02
\]

Thus:

1. \( m = 4 \) (compounding periods per year).
2. \( n = 38 \) (total compounding periods).
3. \( i = 0.02 \) (interest rate per compounding period in decimal form).

Would you like further details or explanations?

Here are some related questions you might consider:
1. How would the values of \( m \), \( n \), and \( i \) change if the investment was compounded monthly?
2. What would be the values of \( m \), \( n \), and \( i \) for an annual interest rate of 6% compounded semi-annually over 10 years?
3. How does the time period \( t \) affect the value of \( n \)?
4. What is the formula to calculate the final amount \( A \) given the principal \( P \), rate \( r \), time \( t \), and compounding frequency \( m \)?
5. How does the compounding frequency \( m \) affect the final amount \( A \) in the long term?
6. Can you derive the formula for effective annual rate (EAR) given the nominal rate and compounding frequency?
7. What happens to \( n \) and \( i \) if the investment was for a period of 15 years instead of 9.5 years?
8. How would you round \( i \) if it had more than four decimal places?

**Tip:** Always express the interest rate per compounding period as a decimal to simplify calculations.

Learn how to calculate compound interest with an 8% annual interest rate compounded quarterly over a period of 9.5 years. Understand the concepts of compounding periods per year, total compounding periods, and interest rate per compounding period.

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