Questions: Use the formula for compound amount, not the table, to find the compound amount and the amount of interest earned on 13,000 at 9% compounded annually for 5 years. Use a calculator. The compound amount is . (Round to the nearest cent as needed.)

Use the formula for compound amount, not the table, to find the compound amount and the amount of interest earned on 13,000 at 9% compounded annually for 5 years. Use a calculator.

The compound amount is . (Round to the nearest cent as needed.)

Transcript text: Use the formula for compound amount, not the table, to find the compound amount and the amount of interest earned on $\$ 13,000$ at $9 \%$ compounded annually for 5 years. Use a calculator. The compound amount is $\$$ $\square$ . (Round to the nearest cent as needed.)

Solution

Solution Steps

Step 1: Identify the given values

The principal amount $ P $ is \$13,000, the annual interest rate $ r $ is 9%, and the time $ t $ is 5 years. Since the interest is compounded annually, the number of compounding periods per year $ n $ is 1.

Step 2: Write the compound interest formula

The formula for the compound amount $ A $ is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

Step 3: Substitute the values into the formula

Substitute $ P = 13000 $, $ r = 0.09 $, $ n = 1 $, and $ t = 5 $ into the formula: \[ A = 13000 \left(1 + \frac{0.09}{1}\right)^{1 \cdot 5} \] \[ A = 13000 \left(1 + 0.09\right)^5 \] \[ A = 13000 \left(1.09\right)^5 \]

Step 4: Calculate $ (1.09)^5 $

Using a calculator: \[ (1.09)^5 \approx 1.5386 \]

Step 5: Calculate the compound amount $ A $

Multiply the principal by the result from Step 4: \[ A = 13000 \cdot 1.5386 \approx 20001.80 \]

Step 6: Calculate the interest earned

Subtract the principal from the compound amount: \[ \text{Interest} = A - P = 20001.80 - 13000 = 7001.80 \]