This lab concerns situations modeled by a compounding process. A typical example is the way interest accumulates in a savings account. The first problem builds a "compound interest" calculator. You also build a balance sheet to see the effect of each interest payment.

Problem 1. A sample situation:

Fred Jones places $4000 in a saving account that pays an 9% annual interest rate, compounded quarterly. What is his account balance after one year and how much interest does he make in that year?

To solve this problem we compute the balance in the account after 1 year and find the interest by subtracting the balance from the original deposit. Steps (a)-(c) below place a "Compound Interest Calculator" in cells A1..B12. Place labels in column A, input data in cells B4..B7, and formulas to calculate results in cells B9..B12. The Total number of periods is denoted "Tot#period". In columns D and E the balance at the end of each quarter is computed. Verify the total obtained in cell E9 is the same as the Balance in cell B11.

a. Enter the following text, numbers and formulas into a clean worksheet. Steps (b) and (c) complete the template.

	A	B	C	D	E	F
1	Problem #1
2	Compound interest problem
3
4	Deposit	4000		Totals per Period
5	Rate/yr	0.09		start	=B4
6	Period/yr	4		1	=E5+E5*B$10
7	No.Yrs	1		2
8				3
9	Tot#Period	=B6*B7		4
10	rate/period	=B5/B6
11	final balance
12	interest

b. The formula in cell E5 copies the initial deposit from cell B4. The formula in cell E6 adds the previous balance (the cell above) to the interest for the current period. Now Copy cell E6 to cell range E7..E9 to compute the balance at the end of the remaining quarters.

c. Now we want to use the formula that computes the Final balance (after 4 quarters in this example) straightaway. In cell B11 enter the correct formula from the handout or from the text.

CHECK WITH YOUR INSTRUCTOR TO MAKE SURE THIS FORMULA IS CORRECT. The interest earned (cell B12) is now +B11-B4.

Discussion: Compare the Final balance (in cell E9) with the value computed in cell B11. In a textbox explain the difference in the two methods for obtaining this answer (E9 and B11 should be the same). Save the worksheet and turn in a printout.

Now we want to take advantage of the work we did in Problem 1.

Problem 2. (a) Copy the Compound Interest template and Balance Sheet template (cell range A1..E12) to a new worksheet. Suppose now the interest is compounded daily (banks use 365 days for the year), instead of quarterly, as in Problem 1. Change the appropriate input values to determine how much interest is now earned after one year. In a textbox state the total amount of interest earned and explain why cells E9 and B11 are no longer the same.

(b) Copy the Compound Interest template (cell range A1..B12) to a cell range below your discussion of Part (a). Suppose now the interest is compounded daily (remember 365 days for the year) for two years instead of one year. Change the appropriate input to determine the interest and final balance for this situation. State these amounts and explain why more interest is earned in 2 years than in year 1.

Save this worksheet and turn in a printout of Problem 2.

Problem 3. Copy the template (cells A1..E12) in Problem 1 to a new worksheet. In this problem you are modify the template to illustrate the situation where the initial $4000 is left in the account for five years instead of just one. Keep the interest rate at 9% compounded quarterly. You need to make two changes in the template: first, change the number of years to 5; and second, in column D, you need to list the periods from 1 to 20 and copy the formula in column E to apply to all 20 periods. Construct this new worksheet.

Discussion: In a textbox state the account balance at the end of each year and give the amount of interest earned by the account during each year. Save the worksheet and turn in a print out Problem 3.

In the problems below you only need the Compound Interest template (cells A1..B12). Each calculation should use a separate copy. Give the answer to each question in the form of a sentence.

Problem 4.(a) Suppose you put $1000 in Bank #1, which is offering a savings plan with 6% annual rate, compounded every month. How much interest is earned in one year? State your answer in a sentence supported by data in a template.

(b) A friend has found that Bank #2 is also giving 6% interest, but it compounds every second. How much interest does he earn in one year?

(c) What is the difference in the amount of interest earned at these two banks?

(d) Suppose each bank has total deposits of ten billion dollars. What is the difference in the amount of interest paid by the two banks? [Hint: ten billion is ten million times 1000.] State your answer in sentence form.

Problem 5. At the end of June 2004 the median price of a single-family home in Charleston was $175,000. If home prices have been increasing at an annual rate of 9% for the last decade, what would have been the median price of a home 10 years ago in today's dollars? [Hint: remember that inflation is just a form of compounding.] Explain your strategy for calculating the answer.

Problem 6. The 1975-76 College Catalog lists the total expenses for freshmen in 1975-76 as $2,580 for South Carolina students and $3,230 for Out-of-State students. For 2007-2008 the total expenses for freshmen is $19,595 for South Carolina students and $31,151 for Out-of-State students. Assume that college costs compound at a fixed percentage each year.

(a) Find this annual percentage increase for SC students since 1975-76 and find the annual percentage increase for Out-of-State students over the same period. State your answers in sentence form.

(b) Using the annual percentage increase you found in part (a) estimate the In-state and Out-of-state expenses for students for the year 2009-2010.