259 Lecture 2 Spring 2013 Finance Applications with Excel – Simple and Compound Interest

2 Finance Applications  Excel is a useful tool for working with financial applications that arise in areas such as business, economics, or actuarial science, including:  Simple Interest  Compound Interest  Annuities  Amortization

3 Simple Interest  In order to borrow (invest) money from a bank, we have to pay (are paid) interest on the money, which is usually a percentage of the amount borrowed (invested).  Simple interest is a type of interest that is paid only on the amount borrowed (invested).

4 Simple Interest (cont.)  If we deposit P dollars at an annual interest rate of r%, for a time period t years, then the future value or maturity value of the principal P is given by  A = P(1+r*t).  Note that the interest is given by  I = P*r*t.

5 Simple Interest (cont.)  Example 1: For which of the following loans would we end up paying less interest?  (a) $10,000 borrowed for 1 year at 7% interest.  (b) $9,000 borrowed for 11 months at 8% interest.

6 Simple Interest (cont.)

7 Using Scenarios  We can also use Scenarios to compare loans!  Construct a “Simple Interest Calculator” in Excel!  Click on the Data tab and choose What-If Analysis from the Data Tools group to pull up the Scenario Manager.

8 Using Scenarios (cont.)  In the Scenario Manager, choose “Add” to add a new scenario.  Choose “Loan 1” as the Scenario name and choose cells B2:B4 as the Changing cells.  Change any cell values you wish for the scenario and click OK.

9 Using Scenarios (cont.)  Repeat the above steps to add more scenarios.  Add a Scenario called “Loan 2” with appropriate data from Example 1.  Use or =11/12 for the time period instead of 11/12. (Why?)  Choose “Summary” to get a summary table of all the scenarios!

10 Using Scenarios (cont.)

11 Present Value  Suppose we wish to have a certain amount of money at a future date, based on money deposited today.  The amount needed today is called the present value of the future amount.

12 Present Value (cont.)  If future amount A is obtained by investing amount P today at simple interest rate r% for t years, then present value P can be found from the future value formula above by solving for principal P:  P = A/(1+r*t)

13 Present Value (cont.)  Example 2: Tuition of $6000 will be due when the spring semester starts in 5 months.  What amount should be deposited today at 3% interest to have enough to cover the tuition?

14 Present Value (cont.)  One way to solve this problem is to directly calculate the present value of the $6000 using the formula P = A/(1+r*t).  We find P = 6000/(1+0.03*(5/12)) = dollars.  Another way is to guess choices for principal P in the “Simple Interest Calculator” we made in Excel until the future value A is $6000.  A third way is to use the Excel’s Goal Seek tool, which attempts to solve problems with one variable.

15 Goal Seek  Reset cell B2 to a principal of 5000 dollars.  Click on What-If Analysis=>Goal Seek.  In the Goal Seek dialog box, Set cell B5, To value 6000, By changing cell B2.  Click OK and Excel will try to find a solution iteratively.

16 Goal Seek (cont.)  In this case, a solution is found!  Choose OK to keep the solution, which is what we calculated “by hand” above!  How about if we want to have the entire tuition payment in 4 months?  Repeat with a time period of 4 months to get present value of $

Goal Seek (cont.)  Now, using the 4 month solution we just found, try starting with an interest rate of 8% and changing the time period (via Goal Seek) to get a future value of A = $6000.  Note that Goal Seek requires a value (i.e. number), not a formula (such as =4/12) in the changing cell. 17

18 Compound Interest  Simple interest is usually used for loans or investments of one year or less.  For longer investment periods, compound interest is used.  In this case, interest is charged (paid) on both interest and principal!

19 Compound Interest (cont.)  Suppose you put $10,000 into a bank account earning 5% annual compound interest.  After 1 year, the account will have: 10, ,000*(0.05)= 10,000*(1+0.05) dollars  After 2 years, the account will have: 10,000(1+0.05) + 10,000(1+0.05)*(0.05) = 10,000*(1+0.05) 2 dollars ……  After n years, the account will have: 10,000(1+0.05) n dollars.

20 Compound Interest (cont.)  In general, if P dollars are deposited for n consecutive compounding periods at an interest rate i per period, the compound amount A is given by  A = P(1+i) n.  Note: As before for simple interest, we also call P the principal or present value as appropriate and call A the future value.

21 Compound Interest (cont.)  Example 3: Construct a table to compare the difference between investing $10,000 at an annual rate of 4% for 5 years with compound interest and investments where the money is compounded annually, quarterly, monthly, daily, and hourly, and every minute!  Which is the best investment?  Is there much of a difference between the last three investments?

22 Compound Interest (cont.)

23 Annuities and Amortization  We’ll look at these next time!

24 References  Finite Mathematics and Calculus with Applications (4 th edition) by Margaret L. Lial, Charles D. Miller, and Raymond N. Greenwell