Using the tables on the following pages, compute the following. Find the...
A) ** future value of investing $5,800 at 6% annual interest compounded semi-annually for 6 years.
First, look up the value in the FVIF table for 6% semi-annually, which would be 3% periodic rate
6% 3%
2
 
=    

for 6 years (or 12 periods)... 1.4258.

To calculate the future value (FV) of an investment using the future value interest factor (FVIF) table, follow these steps:

### Given:
- **Principal (P):** $5,800
- **Annual Interest Rate (r):** 6% (compounded semi-annually)
- **Number of Years (t):** 6 years
- **Compounding Periods per Year (m):** 2 (semi-annually)

### Step 1: Determine the Periodic Interest Rate
Since the interest is compounded semi-annually:
\[
\text{Periodic Interest Rate} = \frac{\text{Annual Interest Rate}}{2} = \frac{6\%}{2} = 3\%
\]

### Step 2: Determine the Total Number of Periods
Since there are 2 compounding periods per year:
\[
\text{Total Number of Periods} = \text{Years} \times \text{Compounding Periods per Year} = 6 \times 2 = 12 \text{ periods}
\]

### Step 3: Look Up the FVIF
From the FVIF table, for 3% over 12 periods, the FVIF is given as **1.4258**.

### Step 4: Calculate the Future Value (FV)
Use the formula:
\[
\text{FV} = \text{Principal} \times \text{FVIF}
\]
Substituting the values:
\[
\text{FV} = 5,800 \times 1.4258 = 8,269.64
\]

### Final Answer:
The future value of investing $5,800 at 6% annual interest compounded semi-annually for 6 years is **$8,269.64**.

Would you like more details on any step, or do you have any questions?

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Here are 5 follow-up questions related to the topic:
1. How would the future value change if the interest were compounded quarterly instead of semi-annually?
2. What is the formula for calculating the future value without using the FVIF table?
3. How does the frequency of compounding affect the future value of an investment?
4. Can you explain the difference between simple interest and compound interest?
5. How would the future value be affected if the interest rate were 8% instead of 6%?

**Tip:** When calculating the future value of an investment, the frequency of compounding plays a significant role in determining the final amount. The more frequently interest is compounded, the higher the future value will be.

Using the tables on the following pages, compute the following. Find the future value of investing $5,800 at 6% annual interest compounded semi-annually for 6 years.

Learn how to calculate the future value of investing $5,800 at 6% annual interest compounded semi-annually for 6 years. This step-by-step guide covers essential concepts such as the periodic interest rate, total number of periods, and how to use the FVIF table. Suitable for students in Grades 9-12.

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