The following investment requires table factors for periods beyond the table. Using Table 11-1, create the new table factor, rounded to five places, and calculate the compound amount (in $, rounded to the nearest cent.)
Principal	Time
Period (years)	Nominal
Rate (%)	Interest
Compounded	New Table
Factor	Compound
Amount
$16,000	29	8	annually	 	$

To solve this, we'll need to compute the compound amount for a principal of $16,000, with an interest rate of 8%, compounded annually over 29 years. 

The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $A$ is the compound amount.
- $P$ is the principal amount ($16,000).
- $r$ is the nominal annual interest rate (8% or 0.08).
- $n$ is the number of times the interest is compounded per year (for annually, $n = 1$).
- $t$ is the time the money is invested or borrowed for, in years (29 years).

### Step 1: Calculate the new table factor

The table factor corresponds to the value of $\left(1 + \frac{r}{n}\right)^{nt}$, which in this case simplifies to:

\[
\left(1 + \frac{0.08}{1}\right)^{1 \times 29} = (1.08)^{29}
\]

Let's calculate this value.

The new table factor for this investment is approximately **9.31727** (rounded to five decimal places).

### Step 2: Calculate the compound amount

Now, we use the formula for compound interest:

\[
A = P \times \text{Table Factor}
\]

Substituting the values:

\[
A = 16,000 \times 9.31727
\]

Let's compute the compound amount.The compound amount for this investment is approximately **$149,076.40**, rounded to the nearest cent.

Would you like any further details or explanations?

### Related Questions:
1. How would the result change if the interest were compounded semi-annually instead of annually?
2. What would happen if the interest rate increased to 9%?
3. How is the table factor calculated for different compounding periods, such as monthly or quarterly?
4. What is the total interest earned over the 29 years in this scenario?
5. How would a shorter investment period (e.g., 20 years) affect the compound amount?

**Tip**: Longer time periods exponentially increase compound growth, especially with higher interest rates, due to the power of compounding.

The following investment requires table factors for periods beyond the table. Using Table 11-1, create the new table factor, rounded to five places, and calculate the compound amount (in $, rounded to the nearest cent.) Principal: $16,000; Time Period (years): 29; Nominal Rate (%): 8; Interest Compounded: annually.

Learn how to calculate compound interest for a $16,000 investment over 29 years with an 8% annual interest rate. This example explains how to find the table factor and compound amount using the formula A = P(1 + r/n)^(nt), perfect for students in Grades 10-12.

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