Final answer:
The bond interest rate for Shannon's investment is 1.60083%, calculated by dividing the annual interest payment by the bond's face value after accounting for the purchase price and maturity value.
Step-by-step explanation:
The bond interest rate is the rate paid by bond issuers on the bond's face value. In this case, we need to find the annual interest that Shannon earns on her bond investment. Shannon purchased the bond for $1,142.38, and it will mature at $1,200 after 3 years, with an 11% yearly yield compounded annually.
We can calculate the annual interest payment using the formula for the future value of a single sum:
- Calculate the total amount Shannon will receive at maturity: $1,200.
- Subtract the purchase price from the maturity value to find the total interest received over the life of the bond: $1,200 - $1,142.38 = $57.62.
- Since the bond matures in 3 years, divide the total interest by 3 to find the annual interest payment: $57.62 / 3 = $19.21.
- The bond's face value is $1,200. To find the interest rate, divide the annual interest payment by the bond's face value: $19.21 / $1,200 = 0.0160083, or 1.60083%.
Therefore, the bond interest rate that Shannon receives is 1.60083%.