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| Problem: |
To buy a computer, Raquel borrowed $3,000 at 9%
interest for 4 years. How much money did she have to pay back? |
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| 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.
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| 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.
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| 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 |
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Now that we have a procedure and a formula, we can solve the problem above.
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| Problem: |
To buy a computer, Raquel borrowed $3,000 at 9% interest
for 4 years. How much money did she have to pay back? |
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| Solution: |
Principal = $3,000, Interest rate = 0.09 and Time = 4 |
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I = P*R*T |
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I = (3000)*(0.09)*(4) = $1,080.00
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| Answer: |
Raquel had to pay back $3,000 in principal plus
$1,080 in interest for a total of $4,080.00. |
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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.
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| 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? |
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| Solution: |
P = $1,200, R = 0.18 and T = 0.75
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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.
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I = P*R*T |
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I = (1200)*(0.18)*(0.75) = 162.00 |
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| Answer: |
Kevin paid $162.00 in interest. |
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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.
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| 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? |
 |
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| Solution: |
P = $500, R = 0.055 and T = 1
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I = P*R*T |
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I = (500)*(0.055)*(1) = $27.50 |
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| Answer: |
Isabella earns $27.50 per year in interest from
her local bank. |
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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.
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| 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? |
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| Solution: |
P = $38,000, R = 7.25% and T = 10 |
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I = P*R*T |
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I = (38000)*(.0725)*(10) = $27,550.00 |
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| 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? |
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| Solution: |
P = $1000, I = 0.04 and T = 0.25 |
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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. |
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I = P*R*T |
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I = (1000)*(0.04)*(0.25) = $10.00
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| Answer: |
Julia will have $1,000 in principal plus $10 of
interest earned for a total of $1,010.00. |
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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%.
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| 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 |
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|
| 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 |
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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?
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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
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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.
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1.
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Matilda invested $5,000 at a rate of 7.5%. How much did she have
after 6 months?
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2.
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Aaron borrowed $200 to finance a VCR at a rate of 8.25% for 1
years. How much did he repay altogether?
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3.
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Sam deposited $400 into a savings account that earned 4%
interest per year. How much money did he have after 2.5 years?
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4.
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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?
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5.
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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?
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Interactive Math Goodies Software
