Simple Interest
If an amount of money,
P, the principal, is invested for a period of
t years at an annual interest rate
r, the amount of interest,
I, earned is
I=Prt
where
IPrt====interestprincipalratetime
Interest earned according to this formula is called simple interest.
The formula we use to calculate simple interest is
example
Find the simple interest earned after
3 years on
$500 at an interest rate of
\text{6%.}
Solution
Organize the given information in a list.
\begin{array}{ccc}\hfill I& =& ?\hfill \\ \hfill P& =& \text{$500}\hfill \\ \hfill r& =& \text{6%}\hfill \\ \hfill t& =& \text{3 years}\hfill \end{array}
We will use the simple interest formula to find the interest.
Write the formula. |
I=Prt |
Substitute the given information. Remember to write the percent in decimal form. |
I=(500)(0.06)(3) |
Simplify. |
I=90 |
Check your answer. Is $90 a reasonable interest earned on $500 in 3 years? |
|
In 3 years the money earned 18\text{%}. If we rounded to 20\text{%}, the interest would have been 500(0.20) or $100. Yes, $90 is reasonable. |
|
Write a complete sentence that answers the question. |
The simple interest is $90. |
example
Find the principal invested if
$178 interest was earned in
2 years at an interest rate of
\text{4%.}
Answer:
Solution
Organize the given information in a list.
\begin{array}{ccc}\hfill I& =& \text{$178}\hfill \\ \hfill P& =& ?\hfill \\ \hfill r& =& \text{4%}\hfill \\ \hfill t& =& \text{2 years}\hfill \end{array}
We will use the simple interest formula to find the principal.
Write the formula. |
I=Prt |
Substitute the given information. |
178=P(0.04)(2) |
Divide. |
0.08178=0.080.08P |
Simplify. |
2,225=P |
Check your answer. Is it reasonable that $2,225 would earn $178 in 2 years? |
|
I=Prt |
|
178=?2,225(0.04)(2) |
|
178=178✓ |
|
Write a complete sentence that answers the question. |
The principal is $2,225. |
example
Find the rate if a principal of
$8,200 earned
$3,772 interest in
4 years.
Answer:
Solution
Organize the given information.
IPrt====$3,772$8,200?4 years
We will use the simple interest formula to find the rate.
Write the formula. |
I=Prt |
Substitute the given information. |
3,772=8,200r(4) |
Multiply. |
3,772=32,800r |
Divide. |
32,8003,772=32,80032,800r |
Simplify. |
0.115=r |
Write as a percent. |
\text{11.5%}=r |
Check your answer. Is 11.5\text{%} a reasonable rate if $3,772 was earned in 4 years? |
|
I=Prt |
|
3,772=?8,200(0.115)(4) |
|
3,772=3,772✓ |
|
Write a complete sentence that answers the question. |
The rate was 11.5\text{%}. |