Savings and Loans: Problem Solving and Using Scroll Bars

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1 activity 10.1 Savings and Loans: Problem Solving and Using Scroll Bars In the first part of this activity, you will identify problem-solving techniques. In the second part of this activity, you will learn how to create a scroll bar using Excel and then use it to solve problems about savings and loans. 1. Identify all problem-solving techniques used in #1 of Activity 6.1 (where you decided which of the magic genie s two offers to choose). For each technique you identify, describe where in the activity it was used.

2 Activity 10.1: Savings and Loans Describe a problem (you can use one solved previously, or you can construct one) that can be solved using the stated problem-solving technique (by itself or in combination with other techniques): a. Problem-solving technique 2b. Draw a picture, graph, or diagram. b. Problem-solving technique 3. Examine a simple case or try several special cases. c. Problem-solving technique 5. Work backward. 3. In the next part of this activity, you will create an Excel scroll bar to see how interest grows in a savings account.

3 498 Excel Activities Scroll Bars A scroll bar is an exciting addition to a spreadsheet that can allow you to vary a value easily. You can vary, for example, the interest rate on an investment in an account over an interval from 1 percent to 20 percent to see how the total amount in the account is changing dynamically. Instructions to Use Excel to Create a Scroll Bar a. b. c. d. e. f. You ll first set up a spreadsheet to calculate the interest and total money in the account with an investment of $1000 over a 15-year period. In cell C1, enter the label Interest Rate as a Percent and in cell C2 enter =1. In cell B1, enter the label Interest Rate as a Decimal and in cell B2 enter =C2/100. (The value in cell C2, which is the interest rate as a percent, will be linked to the scroll bar. The value in cell B2 is the interest rate as a decimal.) In cells A4, B4, and C4, enter the labels Year, Interest, Total, respectively. In cell A5, enter 0; in A6 enter 1. Highlight both of these cells and drag down to cell A20 to represent 15 years. In cell C5, enter $ , which will be the starting amount in the account. In cell B6, enter =$B$2*C5. (Note that you can type =B2 and then press the F4 function key to get the result $B$2.) In cell C6, enter the formula, =C5 + B6. Highlight cells B6 and C6 and drag down to show the interest and total for each of the 15 years. Next you will sketch a scatterplot of x = Year and y = Total. You will need to highlight the label and values in the Year column, press Ctrl, release the left mouse button, and then go to the Total column and highlight the label and values in this column. Now using the Insert tab, create the scatterplot, with the points connected by a line. Choose appropriate titles for the axes and chart.

4 Activity 10.1: Savings and Loans 499 g. h. i. j. k. l. To use a scroll bar, you will need to access the Developer tab. If the Developer tab is not shown on top of the menu ribbon, use the following instructions to load it. Click the Office Button. Then click Excel Options (at the bottom of the pop-up window). Choose Popular on the left menu box, check Show Developer tab in the Ribbon, and then click OK. Click on the Developer tab and then go to the Controls group and click on the small arrow under Insert. On the pop-up menu, under ActiveX Controls, find the Scroll bar icon. (Look for the small picture with the up and down arrows and check that the words Scroll bar (ActiveX Control) appear when you place the cursor over it. Click on this icon. The Design Mode icon in the Controls group will light up and the cursor becomes a thin plus sign. Move the cursor (the plus sign) to the spot where you want the scroll bar. Press and hold the left mouse button. Drag the mouse horizontally to the right to create a horizontal scroll bar, or drag it down to create a vertical scroll bar. When the scroll bar is the size you want, release the mouse button. You should see small open circles, called handles, around the outside of the scroll bar. With the handles still showing, move the cursor to the Controls group of the Ribbon and click on Properties. This brings up the Properties box containing a list of properties in alphabetical order. You will need to fill in three values: LinkedCell, Max, and Min. Linked cell refers to the cell where you have placed the value you want to change when you scroll. Point to the words LinkedCell, click, and type C2 here. Point to Min, click, and enter 1, and then point to Max, click, and enter 20. Move the cursor to a cell outside the Properties box and click. To close the Properties box, click the x in the upper-right corner of the box. Click on Design mode in the Controls group (which should still be highlighted) to exit Design mode. You are almost ready to use the scroll bar you designed. You need to change the scale on the y-axis of the scatterplot so the scaling is not automatic, but is fixed. On your finished graph, point to any number on

5 500 Excel Activities the y-axis and right-click; then click on Format axis. In the Axis Options window, click on Fixed for Minimum; then enter 1000 in the Minimum box. Also click on Fixed for Maximum and enter in the box. Click Close. (Fixing the scale will allow you to see how the graph changes as the scroll bar changes the value of the interest rate.) m. You are now ready to move the little box on the scroll bar to increase or decrease the value of the interest rate. This will in turn alter the Total column of the spreadsheet and change the graph. 4. Describe how the graph changes as the scroll bar moves. You can also use a scroll bar to solve Josh s problem (see Example 10.5 in Topic 10). To do this, you will first create a graph of the monthly balance remaining, and then you can change the monthly payment using the scroll bar. Here is how: 5. Go to a new sheet in your Excel workbook. Set up the new sheet as follows: a. b. In cell A1, enter the label APR as a Decimal, and in cell A2, enter 0.06, the loan s APR (as a decimal) for the loan from the credit union. In cell B1, enter the label Monthly Interest Rate, and in cell B2 enter = A2/12, the monthly interest rate. In cell C1, enter the label Tentative Payment and in cell C2, enter $100.00, a tentative payment amount (this will be attached to the scroll bar and moved until you find the payment needed to pay off the loan in 60 months).

6 Activity 10.1: Savings and Loans 501 c. d. e. f. g. h. i. j. In cells A4, B4, and C4, enter Year, Balance Last Month, and Balance This Month, respectively. In column A beginning at cell A5, fill in numbers 1 through 60 (for the 60 months in 5 years). In cell B5, enter $ (this is the starting loan principal or balance at the end the month before you start payments). In cell C5 enter =B5 + B5*$B$2 $C$2 to calculate the loan balance after one month, that is, at the end of the first month. In cell B6, enter =C5. Drag to fill in columns B and C up to month 60. Create a graph that shows balance this month as a function of year. Because you are setting up a scroll bar, you will want to format the y-axis so scaling is fixed. Create a scroll bar with a LinkedCell of C2 (so the payment can be changed by scrolling), with a Min of 0, and a Max of How would you know from the graph that the choice of monthly payment in C5 is the correct one (or a good approximation of it) to pay off the debt in five years? Write the correct amount here. 7. Use the same spreadsheet, changing the interest rate, principal, and compounded period as appropriate, to find all the information needed to solve Josh s problem. Explain how you found the information.

7 502 Excel Activities 8. Identify which problem-solving techniques (see the list in Topic 10) you used to solve Josh s problem in this activity. Compare the techniques used here with the techniques used to solve the same problem in the examples in Topic 10. Which techniques were used in both solutions? Which were used in one and not the other? Summary In this activity, you worked with several problem-solving techniques and looked for situations where specific techniques could be used. You learned how to create a scroll bar in Excel to see how the interest paid and the accumulated total in a savings account change for different annual interest rates. Finally, you used a scroll bar to solve the loan decision problem stated in Example 10.5 and solved in Topic 10.

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