The simple interest on an investment is directly proportional to the amount of the investment.By investing $5800 in a municipal bond, you obtained an interest payment of $221.25 after 1 year.Find a mathematical model that gives the interest I for this municipal bond after 1 year in terms of the amount invested P.(Round your answer to three decimal places.)
A) $I = 26.215 P$
B) $I = 221.25 P$
C) $I = 0.038 P$
D) $I = 1,283,250 P$
E) $I = 5800 P$

Question

The simple interest on an investment is directly proportional to the amount of the investment.By investing $5800 in a municipal bond, you obtained an interest payment of $221.25 after 1 year.Find a mathematical model that gives the interest I for this municipal bond after 1 year in terms of the amount invested P.(Round your answer to three decimal places.)  
A) $I = 26.215 P$
B) $I = 221.25 P$
C) $I = 0.038 P$
D) $I = 1,283,250 P$
E) $I = 5800 P$

Quizplus · Accepted Answer

The interest is directly proportional to the principal amount, so $I = kP$, where $k$ is the constant of proportionality. Given $I = 221.25$ for $P = 5800$, we find $k = \frac{221.25}{5800} = 0.038$. Therefore, the model is $I = 0.038P$.

The Simple Interest on an Investment Is Directly Proportional to the Amount