# Simple Interest Problem: To buy a computer, Raquel borrowed \$3,000 at 9% interest for 4 years. How much money did she have to pay back?

Analysis: When money is borrowed, interest is charged for the use of that money over a certain period of time. The amount of interest charged depends on the amount of money borrowed, the interest rate and the length of time for which the money is borrowed.

Definitions: Principal is the amount of money borrowed. The interest rate is given as a percent. Time is the length of time in years for which the money was borrowed.

Procedure: To find interest, take the product of the principal, the interest rate and the time. Thus, the formula for finding interest is:

Interest = Principal * Rate * Time which is also written as I = P*R*T

Now that we have a procedure and a formula, we can solve the problem above. Problem: To buy a computer, Raquel borrowed \$3,000 at 9% interest  for 4 years. How much money did she have to pay back?

Solution: Principal = \$3,000, Interest rate = 0.09 and Time = 4

I = P*R*T

I = (3000)*(0.09)*(4) = \$1,080.00

Answer: Raquel had to pay back \$3,000 in principal plus \$1,080 in interest for a total of \$4,080.00.

Remember that interest is the charge for borrowing the money. So Raquel had to pay back the original amount borrowed (principal) AND the interest. Let's look at some more examples of interest. Example 1: When Kevin bought a new office phone, he borrowed \$1,200 at a rate of 18% for 9 months. How much interest did he pay?

Solution: P = \$1,200, R = 0.18 and T = 0.75

Remember that the interest formula asks for the time in years. However, the time was given in months. So to get the time in years we represent 9 months as 9/12 of a year, or 0.75.

I = P*R*T

I = (1200)*(0.18)*(0.75) = 162.00

Answer: Kevin paid \$162.00 in interest.

In the problem and example above, money was borrowed and interest was paid for borrowing that money. A person can also earn interest on money invested. Let's look at an example of this. Example 2: Isabella deposited \$500 into a savings account at a local bank that earned 5 % interest per year. How much interest does she earn per year?

Solution: P = \$500, R = 0.055 and T = 1

I = P*R*T

I = (500)*(0.055)*(1) = \$27.50

Answer: Isabella earns \$27.50 per year in interest from her local bank.

In Example 2, the bank was the borrower and Isabella was the lender. Let's revise our definition of interest so that it applies to all of these problems.

Interest is the amount of money the lender is paid for the use of his/her money. Interest is the money you pay to use someone else's money. In either case, the more money being used and the longer it is used for, the more interest must be paid. Let's look at some more examples of interest. Example 3: Jodi owes \$38,000 in students loans for college. The interest rate is 7.25% and the loan will be paid off over 10 years. How much will Jodi pay altogether?

Solution:

P = \$38,000, R = 7.25% and T = 10

I = P*R*T

I = (38000)*(.0725)*(10) = \$27,550.00

Answer: Jodi will have to pay \$38,000 in principal plus \$27,550 in interest for a total of \$65,550.00. Example 4: Julia put \$1,000 into a savings account that earns 4% in interest. How much will she have after 3 months?

Solution: P = \$1000, I = 0.04 and T = 0.25

Remember that the interest formula asks for the time in years. However, the time was given in months. So to get the time in years we represent 3 months as 3/12 of a year, or 0.25.

I = P*R*T

I = (1000)*(0.04)*(0.25) = \$10.00

Answer: Julia will have \$1,000 in principal plus \$10 of interest earned for a total of \$1,010.00.

In each of the examples above, the interest rate was applied only to the original principal amount in computing the amount of interest. This is known as simple interest. When the interest rate is applied to the original principal and any accumulated interest, this is called compound interest. Simple and compound interest are compared in the tables below. In both cases, the principal is \$100.00 is and the interest rate is 7%.

 Simple Interest Year Principal Interest Ending Balance 1 \$100.00 \$7.00 \$107.00 2 \$100.00 \$7.00 \$114.00 3 \$100.00 \$7.00 \$121.00 4 \$100.00 \$7.00 \$128.00 5 \$100.00 \$7.00 \$135.00
 Compound Interest Year Principal Interest Ending Balance 1 \$100.00 \$7.00 \$107.00 2 \$107.00 \$7.49 \$114.49 3 \$114.49 \$8.01 \$122.50 4 \$122.50 \$8.58 \$131.08 5 \$131.08 \$9.18 \$140.26

As you can see, compound interest can end up being higher than simple interest for the same principal and the same rate. If you were borrowing money, would you want to pay simple interest or compound interest? If you were lending or investing money, would you want to earn simple interest or compound interest?

Summary: Interest is the amount of money the lender is paid for the use of his/her money. Interest is the money you pay to use someone else's money. In either case, the more money being used and the longer it is used for, the more interest must be paid. So whether you are borrowing or lending (investing)  money, interest is found by taking the product of the principal, the interest rate and the time in years. The formula for finding simple interest is:

Interest = Principal * Rate * Time which is also written as I = P*R*T

### Exercises

Directions: Each problem below involves simple interest. Solve each problem below by entering a dollar amount with cents. For each exercise below, click once in the ANSWER BOX, type in your answer and then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

 1 Matilda invested \$5,000 at a rate of 7.5%. How much did she have after 6 months? ANSWER BOX:  \$  RESULTS BOX:
 2 Aaron borrowed \$200 to finance a VCR at a rate of 8.25% for 1 years. How much did he repay altogether? ANSWER BOX:  \$  RESULTS BOX:
 3 Sam deposited \$400 into a savings account that earned 4 % interest per year. How much money did he have after 2.5 years? ANSWER BOX:  \$  RESULTS BOX:
 4 Gabriella borrowed \$3,600 to finance a large-screen television at a rate of 6.25% for 4.75 years. How much interest did she pay? ANSWER BOX:  \$  RESULTS BOX:
 5 Matthew deposited \$900 into a certificate of deposit with a rate of 1.5% for 6 months. How much money did he have in the account after 6 months? ANSWER BOX:  \$  RESULTS BOX: