How Are Inputs and Outputs Related Through A Model?

When working with a model, you need to pay careful attention to the units on each variable.

Problems 1 The number y (in millions) of women in the workforce is given by the function \displaystyle y=0.006{{x}^{2}}-0.018x+5.607 where x is the number of years after 1900.

a. Find the value of y when x = 44. Explain what this means.

b. Use the model to find the number of women in the workforce in 2010.

The solution above is the correct strategy, but there is an error…can you find the error?

How Do I Find The Payment On A Loan That Is Amortized?

A couple of you have had trouble finding the payment properly. I am not sure whether this is a calculator issue (there is a screen capture for the payment in Question 3 of Section 5.4) or a formula issue. Often I see people using the interest rate for i instead of the interest rate per period. Remember, since i is the interest rate per period you need to divide it by the number of periods in a year.

Here is an additional example of finding the payment and then using it to construct an amortization table.

How Do I Find The Rate For A Sinking Fund?

To find the rate for a sinking fund, you needed to use a graph or the TVM Solver on a TI graphing calculator to find the interest rate on a sinking fund. Let’s look at the most basic way of doing this by graphing.

Problem Find the interest rate needed for a sinking fund to accumulate 25,600 dollars in five years with monthly payments (made at the end of the month) of 400 dollars.

Solution Since this problem indicates that payments are being made, we need to use the ordinary annuity formula. For a sinking fund, the future value is known, 25600. We also know the payment, 400, and the number of periods, 60:

This is incredibly difficult to solve for i algebraically. Instead, graph each side of the equation and look for a point of intersection. On a graphing calculator we would type y1 = 400*((1+x)^60-1)/x and y2 = 25600 in the window [0, 0.004] by [23500, 27500].

The toughest part is coming up with the window on the graph. Since the x on your calculator represents the interest rate per period, it needs to small like 0 to 0.01 initially. The vertical window is much easier to determine since the second equation is y = 25600, a horizontal line. Simply pick a horizontal window that spans this value.

The annual interest rate is 12 · 0.00217 ≈ 0.02604 or approximately 2.6%.