Math Problem Statement
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 = %
Solution
To determine the annual interest rate , 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:
Where:
- is the total interest earned,
- is the principal (initial cost of the bond),
- is the annual interest rate (in decimal form),
- is the time in years.
In this case:
- (total interest),
- (principal),
- (time in years).
Rearranging the formula to solve for :
Substitute the known values:
To express as a percentage, multiply by 100:
So, the annual interest rate is approximately:
Would you like any further explanation or details on this? Here are 5 related questions you might want to explore:
- How would the interest rate change if the bond lasted for 10 years instead of 7?
- What would be the total interest if the interest rate was compounded annually?
- How can you calculate the future value of this bond if it had compounded interest?
- How would increasing the bond price affect the interest rate?
- 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.
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Math Problem Analysis
Mathematical Concepts
Simple Interest
Algebra
Formulas
I = P * r * t
r = I / (P * t)
Theorems
Simple Interest Theorem
Suitable Grade Level
Grades 10-12
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