 Future Value of Simple Interest and Compounded Interest Investigation

By: Amanda Sawyer

At Charleston Southern University, there is a course called MATH 105 Introduction to Mathematical Structures.  In this course, we discuss many mathematical concepts like Set Theory, Basic Algebra, Logic Theory, Data Analysis, Probability, and Interest.  When we study interest problems, we always go into A) Future Value of Simple Interest and B) Future Value of Compound Interest.  Given some initial amount that we call the principal (P), the number of years you will use this amount (t), and the interest rate per year (r), we can find its future value.  In this assignment, we will investigate different ways of showing the future value of interest using an excel spreadsheet.

A) Future Value of Simple Interest

Let’s first investigation how to solve future value of simple interest.  Let’s define simple interest. Simple interest is the amount of money paid on a loan. It is the easiest type of interest to calculate and understand because its value I = Prt (Simple Interest = Principal x Interest Rate x Time).  Below you will see example of a simple interest problem:

If you deposit \$800 in an account paying 6% simple interest for 4 years, determine the amount of interest earned on the given deposit.

From this, we can find future value of simple interest: When A is the future value, we can see that this amount is just our initial quantity with the addition of simple interest.  An example of a future value of simple interest problem would be:

If you deposit \$1300 in an account paying 10% simple interest for 2 years, determine the future value the deposit.

We can have students study this concept using an Excel Spread Sheet.  In the spreadsheet the students can have the first input as the principal and second input as the time in years.  This way they can see how the interest rate affects the future value.  They can also play with the values to fully see what happens to the amount the longer it is used. You can also look for present value of simple interest using this kind of excel spread sheet.  Present value of simple interest is the initial amount of money you will need to receive a given amount in a given number of years.  For example, a question could ask:

Sam and Diane need to have \$20,000 available in 18 years to pay for their daughter’s first year of college.  Find the lump sum they must invest now if the investment is paying 8% interest rate per year.

When we place these values into an Excel Spread sheet the students can use the guess and check method to check their answer. B) Future Value of Compound Interest

Next, let’s investigate how to find future value of compound interest. Suppose you open an account that pays a guaranteed interest rate, compounded annually.  If you make no further contributions, how much money would you have after t number of years?  We can calculate this information as seen from the table below.

 Year Balance Now P 1 P+rP 2 (P+rP) +r(P+rP)

We can see that a pattern is occurring.  This shows us that we can find a formula for compounded annually interest: However if we wanted to find out the future value of an amount compounded n times a year, we would replace the 1 in the formula with n.  Therefore, our formula for future value of compound interest is: When we study compound interest, we discuss what will happen if the account is compounded quarterly, semiannually, monthly, and daily.  Below is a sample problem that involves finding the future value of compound interest.

If you deposit \$5,000 in an account paying 5% interest, how much money will you receive in 8 years if the account is

a) compounded annually

b) compounded semiannually

c) compounded quarterly

d) compounded monthly

e) compounded daily

Again, we can use a spread sheet to study this behavior.  If we allow the first three columns to be the principal, interest rate and time in years respectively, we can find out the future value of these amounts given its nth value as seen below. From this spread sheet it shows how each amount is increased by the nth value.  Most students assume that the amount will increase drastically from compounded annually to compounded daily, but through the use of this spead sheet we are able to see that the difference is not very large.

We have investaged two ways of solving interest problems using Excel Spead Sheets.  Through the use of these repeating values we can investigae many interseting qualities of interest, and the ones that I have shown are just the beginning.