For the given bond, whose interest rate is provided, find the semiannual interest payment and the total interest earned over the life of the bond. $\$ 30,000$ FI National Corporation 18-year bond at $5.5 \%$
A. The semiannual interest payment is $\$ 825$, and the total interest earned is $\$ 29,700$.
B. The semiannual interest payment is $\$ 1,650$, and the total interest eamed is $\$ 29,700$.
C. The semiannual interest payment is $\$ 82,500$, and the total interest earned is $\$ 2,970,000$.
D. The semiannual interest payment is $\$ 75$, and the total interest earned is $\$ 27,000$.
Answer
\(\boxed{\text{Final Answer: The semiannual interest payment is \$ 825, and the total interest earned is \$ 29,700.}}\)
Step 1 ：Given a bond of value $30,000 with an interest rate of 5.5% for 18 years.
Step 2 ：The semiannual interest payment can be calculated by multiplying the bond's value by the interest rate and then dividing by 2. This is because the interest is paid twice a year (semiannually).
Step 3 ：Using the formula, the semiannual interest payment is \( \frac{{30000 \times 0.055}}{2} = \$ 825 \).
Step 4 ：The total interest earned over the life of the bond can be calculated by multiplying the semiannual interest payment by the number of periods. Since the bond is for 18 years and interest is paid semiannually, there are \( 18 \times 2 = 36 \) periods.
Step 5 ：Using the formula, the total interest earned is \( 825 \times 36 = \$ 29,700 \).
Step 6 ：\(\boxed{\text{Final Answer: The semiannual interest payment is \$ 825, and the total interest earned is \$ 29,700.}}\)
