Question 26
6 pts
5
Details
Be sure to clearly show your work for each part of this question.
A broker encourages you to invest in a bond with an issue price of $\$ 5,500$ that pays $3.1 \%$ simple interest annually and matures in 6 years. If you make this investment, find:
a. The amount paid each year in interest payments.
$\$$
b. The total amount earned with the bond.
$\$$
c. Assume interest payments are sent out each year. Find the amount you would receive on the maturity date.
$\$$

Step 1 ：Calculate the annual interest payment using the formula \(I = P \times r \times t\), where \(I\) is the interest, \(P\) is the principal amount, \(r\) is the interest rate, and \(t\) is the time in years.

Step 2 ：The principal amount \(P\) is \(\$5500\), the interest rate \(r\) is \(3.1\%\) or \(0.031\), and the time \(t\) is \(6\) years.

Step 3 ：The annual interest payment is \(I = 5500 \times 0.031 \times 1 = \boxed{170.5}\).

Step 4 ：The total amount earned with the bond is the annual interest payment multiplied by the number of years, which is \(170.5 \times 6 = \boxed{1023.0}\).

Step 5 ：The amount received on the maturity date is the principal amount plus the total interest earned, which is \(5500 + 1023.0 = \boxed{6523.0}\).