The simplest type of interest is called, appropriately, “simple interest.” If you were to loan a friend $1000 to start a business and you both agreed that in one year, the friend would repay you $1060, you would earn $60 interest on that investment.

You would earn $60 simple interest. Simple interest is calculated as a percentage of the initial amount borrowed and does not include any additional earnings.

The percentage of the original loan amount that is paid as simple interest is called the interest rate. In our example, the interest rate on a $1000 loan that requires a $60 interest payment in one year is:

\( {\dfrac {60}{1000}} = \text{0.06 or 6%}\)

Video Source (06:53 mins) | Transcript

The following video shows another example of simple interest and explains how this works with a little more detail.

Video Source (03:44 mins) | Transcript

There are two perspectives on interest. Someone is the lender, and someone is the borrower. From the viewpoint of the lender, interest is great. It allows them to make money on their investment. From the perspective of the borrower, interest can be a big problem. In addition to paying back the original amount of the loan, the borrower must also pay the interest.

The higher the interest rate, the greater the interest payment will be.

Interest Equation: I = Prt

• I = Interest
• P = Principle
• r = Rate (using the decimal form of the %)
• t = Time

Amount Owed = P + I

Additional Resources

• Khan Academy: Intro to Simple Interest (02:45 mins, Transcript)
• Khan Academy: Finding Simple Interest for One Year (05:22 mins, Transcript)
• Khan Academy: Finding Simple Interest for Many Years (08:03 mins, Transcript)

Practice Problems

1. What is the definition for each of the variables in the simple interest formula (I=Prt)? (
   Solution

   x

   Solution:
   I — The amount of interest earned
   P — The original amount of money borrowed for a loan or placed into an investment
   r — The interest rate
   t — The amount of time that the money is invested
   )
2. How much interest will you earn if you invest $500 for three years at a simple interest rate of 4% annually? (
   Solution

   x

   Solution:
   \($60\)
   Details:
   We are calculating the interest on an account earning simple interest, so we will use the formula \(I = Prt.\)
   
   Principle(P): \(${\color{Red}500}\)
   
   Rate in decimal form(r): \({\color{Blue}0.04}\)
   
   Time(t): \({\color{Purple}3}\) years
   
   We will plug that information into our formula \(I = {\color{Red}P}{\color{Blue}r}{\color{Purple}t}\):
   
   I = \({\color{Red}500}{\color{Blue}(0.04)}{\color{Purple}3}\)
   
   I = \(60\)
   
   So we earned \($60\) in simple interest over 3 years.
   )
3. How much interest will you earn if you invest $1000 for seven years at a simple interest rate of 8% annually? (
   Solution

   x

   Solution:
   \($560\)
   )
4. What is the total amount of money that you will have at the end of the four years if you invest $2000 for four years at a simple interest rate of 8% annually? (
   Solution

   x

   Solution:
   \($2,640\)
   Details:
   We are calculating the total amount of money that we will have after 4 years.
   
   Step 1- Find the amount of interest earned: We are earning simple interest, so we will use the formula \(I = Prt\)
   
   Principle(P): \(${\color{Red}2000}\)
   
   Rate in decimal form(r): \({\color{Orange}0.08}\)
   
   Time(t): \({\color{Purple}4}\) years
   
   We will plug that information into our formula \(I = {\color{Red}P}{\color{Orange}r}{\color{Purple}t}:\)
   
   I = \({\color{Red}2000}{\color{Orange}(0.08)}{\color{Purple}4}\)
   
   I = \({\color{Blue}640}\)
   
   So we earned \($640\) in simple interest over 4 years.
   
   Step 2 - Add the interest earned to the initial amount (principle):
   
   \(A = {\color{Red}P} + {\color{Blue}I}\)
   
   \(A = {\color{Red}2000} + {\color{Blue}640}\)
   
   A = \($2640\)
   )
5. What is the total amount of money that you will have at the end of the six years if you invest $900 for six years at a simple interest rate of 7% annually? (
   Solution

   x

   Solution:
   \($1,278\)
   )

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