Simple interest

the simple interest received from investment is directly proportional to the amount of the investment. By investing $4000 in a municipal bond you obtain interest of $280 at the end of 1year. Find a mathematical model that gives the interest I at end of 1year in terms of the amount P.

See:

http://www.jiskha.com/display.cgi?id=1401846779

To find a mathematical model that relates the interest, I, at the end of 1 year in terms of the amount, P, you can use the concept of direct proportionality.

In this case, you are given that the simple interest is directly proportional to the amount of the investment. This means that as the investment amount increases, the interest also increases in the same proportion.

Let's denote the proportionality constant as k. This implies that:

I = kP

Now, you are given a specific scenario where investing $4000 results in an interest of $280 after 1 year. We can use this information to find the value of k.

Substituting the given values into the equation:

$280 = k($4000)

To solve for k, you can divide both sides of the equation by $4000:
280 / 4000 = k

Simplifying the right side:
0.07 = k

So, the constant of proportionality, k, is 0.07.

Now, you can substitute this value back into the equation:

I = 0.07P

Therefore, the mathematical model that gives the interest, I, at the end of 1 year in terms of the amount, P, is I = 0.07P.