Compute the specified quantity.
A 7 year bond costs $3,000 and will pay a total of $200 interest over its lifetime. What is its annual interest rate r (as a percent)? (Round your answer to three decimal places.)
r =
%

To determine the annual interest rate $ r $, we need to use the information provided. The bond has a lifetime of 7 years and will pay a total of $200 in interest. The cost of the bond is $3,000.

The annual interest rate can be calculated using the formula for simple interest:

\[
I = P \times r \times t
\]

Where:
- $ I $ is the total interest earned,
- $ P $ is the principal (initial cost of the bond),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time in years.

In this case:
- $ I = 200 $ (total interest),
- $ P = 3000 $ (principal),
- $ t = 7 $ (time in years).

Rearranging the formula to solve for $ r $:

\[
r = \frac{I}{P \times t}
\]

Substitute the known values:

\[
r = \frac{200}{3000 \times 7}
\]

\[
r = \frac{200}{21000}
\]

\[
r \approx 0.009524
\]

To express $ r $ as a percentage, multiply by 100:

\[
r \approx 0.9524\%
\]

So, the annual interest rate is approximately:

\[
r \approx 0.952\%
\]

Would you like any further explanation or details on this? Here are 5 related questions you might want to explore:

1. How would the interest rate change if the bond lasted for 10 years instead of 7?
2. What would be the total interest if the interest rate was compounded annually?
3. How can you calculate the future value of this bond if it had compounded interest?
4. How would increasing the bond price affect the interest rate?
5. What is the difference between simple interest and compound interest?

**Tip:** Remember, interest rates can be expressed either as percentages or decimals, but calculations often require the decimal form.

A 7 year bond costs $3,000 and will pay a total of $200 interest over its lifetime. What is its annual interest rate r (as a percent)? (Round your answer to three decimal places.)

Learn how to calculate the annual interest rate for a 7-year bond that costs $3,000 and pays a total of $200 in interest. This problem involves simple interest calculations and is suitable for students in Grades 10-12. Step-by-step solution included.

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