Sure, let's break down the calculation of the annual interest step-by-step:
1. Understand the Terms:
- Face Value of the Bond ([tex]$\text{FV}$[/tex]): This is the principal amount that is lent or invested. In this case, it is \[tex]$1,000.
- Annual Interest Rate (\(r\)): This is the percentage of the face value that will be earned as interest in one year. Here, it is $[/tex]8.5\%[tex]$, which can be written as a fraction or a decimal.
2. Convert the Interest Rate to Decimal Form:
- The interest rate is given as $[/tex]8 \frac{1}{2}\%[tex]$.
- First, convert the mixed number to an improper fraction: $[/tex]8 \frac{1}{2} = \frac{17}{2}\%[tex]$.
- To make calculations easier, convert the percentage to a decimal:
\[
8.5\% = \frac{17}{2} \div 100 = \frac{17}{200} = 0.085
\]
3. Formula for Annual Interest (\(I\)):
- The formula to calculate the annual interest is:
\[
I = \text{FV} \times r
\]
4. Plug in the Values:
- Substitute the face value (\$[/tex]1,000) and the decimal form of the interest rate (0.085) into the formula:
[tex]\[
I = 1000 \times 0.085
\][/tex]
5. Perform the Calculation:
- Multiply the face value by the interest rate:
[tex]\[
I = 1000 \times 0.085 = 85.00
\][/tex]
6. Result:
- The annual interest for the bond is \[tex]$85.00.
Thus, the annual interest earned on a bond with a face value of \$[/tex]1,000 and an annual interest rate of [tex]$8 \frac{1}{2}\%$[/tex] is \$85.00.
