Finance Applications with Excel – Simple and Compound Interest 259 Lecture 2 Spring 2017 Finance Applications with Excel – Simple and Compound Interest

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

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).

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.

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.

Simple Interest (cont.)

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.

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.

Using Scenarios (cont.) Repeat the above steps to add more scenarios. Add a Scenario called “Loan 2” with appropriate data from Example 1. Use 0.9167 or =11/12 for the time period instead of 11/12. (Why?) Choose “Summary” to get a summary table of all the scenarios!

Using Scenarios (cont.)

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.

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)

Present Value (cont.) Example 3: 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?

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)) = 5925.93 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.

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.

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 $5940.59.

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.

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!

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 + 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.

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.

Compound Interest (cont.) Example 4: 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?

Compound Interest (cont.)

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

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