Find i​ (the rate per​ period) and n​ (the number of​ periods) for the following annuity.

QuarterlyQuarterly 

deposits of 

​$500500 

are made for 

33 

years into an annuity that pays 

8.58.5​% 

compounded 

quarterlyquarterly.

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Part 1

iequals=enter your response here 

​(Type an integer or decimal rounded to four decimal places as​ needed.)

To find the rate per period $ i $ and the number of periods $ n $ for the given annuity, we'll use the following information:

- **Quarterly deposits:** $ \$500 $
- **Number of years:** 3 years
- **Annual interest rate:** 8.5%
- **Compounding frequency:** Quarterly

### Step 1: Find the rate per period $ i $.

The rate per period $ i $ is calculated by dividing the annual interest rate by the number of compounding periods per year. Since the interest is compounded quarterly, there are 4 compounding periods per year.

\[
i = \frac{r}{4} = \frac{8.5\%}{4} = \frac{0.085}{4} = 0.02125
\]

So, the rate per period $ i $ is **0.0213** (rounded to four decimal places).

### Step 2: Find the number of periods $ n $.

The number of periods $ n $ is calculated by multiplying the number of years by the number of compounding periods per year.

\[
n = 3 \times 4 = 12
\]

So, the number of periods $ n $ is **12**.

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

Here are 8 related questions you might find interesting:
1. How does the compounding frequency affect the rate per period?
2. How would the rate per period change if the compounding were done monthly?
3. What is the formula for calculating the future value of an annuity?
4. How does increasing the number of periods affect the total amount saved in an annuity?
5. How does the frequency of deposits impact the growth of an annuity?
6. What happens to the future value if the interest rate is reduced by half?
7. Can you calculate the future value of this annuity after 3 years?
8. How does the interest rate influence the total interest earned in an annuity?

**Tip:** Always double-check whether the interest rate is given as an annual rate and adjust it according to the compounding frequency to get the rate per period.

Learn how to calculate the rate per period and the number of periods for an annuity with quarterly deposits of $500 over 33 years at 8.5% compounded quarterly. Detailed step-by-step solution included.

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