The simple interest on an investment is directly proportional to the amount of the investment.By investing $2400 in a certain bond issue, you obtained an interest payment of $111.75 after 1 year.Find a mathematical model that gives the interest I for this bond issue after 1 year in terms of the amount invested P.(Round your answer to three decimal places.)
A) $I = 0.047 P$
B) $I = 268,200 P$
C) $I = 21.477 P$
D) $I = 2400 P$
E) $I = 111.75 P$

Question

The simple interest on an investment is directly proportional to the amount of the investment.By investing $2400 in a certain bond issue, you obtained an interest payment of $111.75 after 1 year.Find a mathematical model that gives the interest I for this bond issue after 1 year in terms of the amount invested P.(Round your answer to three decimal places.)  
A) $I = 0.047 P$
B) $I = 268,200 P$
C) $I = 21.477 P$
D) $I = 2400 P$
E) $I = 111.75 P$

Quizplus · Accepted Answer

The interest formula is $I = Prt$, where $P$ is the principal, $r$ is the rate, and $t$ is the time. Given $I = 111.75$ for $P = 2400$, solving for $r$ when $t = 1$ year gives $r = \frac{111.75}{2400} = 0.0465625$, which rounds to $0.047$. Thus, $I = 0.047P$.

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