For the investment situation below, identify the annual interest rate, the length of the investment in years, the periodic interest rate, and the number of periods of the investment.
8% compounded quarterly for 8 years
(a) the annual interest rate
%

(b) the length of the investment in years
yr

(c) the periodic interest rate
%

(d) the number of periods of the investment
periods

Let's break down the given investment scenario: **8% compounded quarterly for 8 years**.

### (a) Annual Interest Rate:
The annual interest rate is given directly in the problem.
- **Annual interest rate = 8%**

### (b) Length of the Investment in Years:
The length of the investment is also provided directly in the problem.
- **Length of investment = 8 years**

### (c) Periodic Interest Rate:
Since the interest is compounded quarterly, we need to find the periodic interest rate by dividing the annual interest rate by the number of compounding periods in a year.
- **Number of compounding periods per year = 4 (quarterly)**
- **Periodic interest rate** = $\frac{8\%}{4} = 2\%$

### (d) Number of Periods of the Investment:
To find the total number of periods, we multiply the number of years by the number of compounding periods per year.
- **Number of periods** = $8 \, \text{years} \times 4 \, \text{periods/year} = 32 \, \text{periods}$

### Summary:
- (a) **Annual interest rate**: 8%
- (b) **Length of investment**: 8 years
- (c) **Periodic interest rate**: 2%
- (d) **Number of periods**: 32 periods

Would you like more details or have any questions?

### Related Questions:
1. What would the periodic interest rate be if compounded monthly instead of quarterly?
2. How would the number of periods change if the investment duration was extended to 10 years?
3. What is the effect of increasing the compounding frequency on the total interest earned?
4. If the interest rate was increased to 10%, how would the periodic interest rate change?
5. What is the future value of this investment if $1000 is initially invested?

**Tip**: Always remember to divide the annual interest rate by the number of compounding periods to find the periodic interest rate.

For the investment situation below, identify the annual interest rate, the length of the investment in years, the periodic interest rate, and the number of periods of the investment. 8% compounded quarterly for 8 years.

Learn how to calculate the annual interest rate, periodic interest rate, and total number of periods for an investment compounded quarterly at 8% over 8 years. This detailed guide includes key formulas, step-by-step explanations, and real-life applications. Perfect for high school students studying finance and math.

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