The simple interest on an investment is directly proportional to the amount of the investment. By investing $4250 in a certain bond issue, you obtained an interest payment of $106.25 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.
I=
I = kA
when A = 4250, then I = 106.25
106.25 = k(4250)
k = 106.25/4250 = .025
I = .025A
thank you :)
45%
I = P * (106.25/4250)
But let me tell you, this bond is so laid back. It's just chilling there, paying its 1-year interest like it's no big deal.
To find a mathematical model that gives the interest I for this bond issue after 1 year in terms of the amount invested P, we need to use the concept of direct proportionality.
In direct proportionality, two quantities are related in such a way that when one quantity increases, the other also increases by the same factor. In this case, the interest amount (I) is directly proportional to the amount invested (P).
Using this information, we can write the proportionality equation as:
I = kP
Where I represents the interest amount, P represents the amount invested, and k is a constant of proportionality.
To determine the value of k, we can use the given information. It is stated that by investing $4250, you obtained an interest payment of $106.25 after 1 year.
Substituting these values into the equation, we get:
106.25 = k * 4250
To solve for k, divide both sides of the equation by 4250:
k = 106.25 / 4250
k = 0.025
Now that we have the value of k, we can substitute it back into the proportionality equation:
I = 0.025P
Therefore, the mathematical model that gives the interest I for this bond issue after 1 year in terms of the amount invested P is:
I = 0.025P