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The principal [tex]$P$[/tex] is borrowed at a simple interest rate [tex]$r$[/tex] for a period of time [tex][tex]$t$[/tex][/tex]. Find the simple interest owed for the use of the money. Assume there are 360 days in a year.

[tex]P = \$1000[/tex], [tex]r = 2.0\%[/tex], [tex]t = 9 \text{ months}[/tex]

The simple interest owed for the use of the money is [tex]\$\square[/tex] (Round to the nearest cent as needed.)


Sagot :

To find the simple interest owed for the use of the money, we will use the simple interest formula:

[tex]\[ I = P \times r \times t \][/tex]

where:
- [tex]\( I \)[/tex] is the simple interest,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( r \)[/tex] is the interest rate,
- [tex]\( t \)[/tex] is the time period in years.

Given the values:
- [tex]\( P = \$1000 \)[/tex],
- [tex]\( r = 2.0\% \)[/tex],
- [tex]\( t = 9 \)[/tex] months.

First, we need to convert the interest rate from a percentage to a decimal. Since 2.0% is the same as 2.0 out of 100, we convert it by dividing by 100:
[tex]\[ r = \frac{2.0}{100} = 0.02 \][/tex]

Next, we need to convert the time period from months to years. There are 12 months in a year, so we have:
[tex]\[ t = \frac{9}{12} \text{ years} \][/tex]

Now, substitute the values into the simple interest formula:
[tex]\[ I = 1000 \times 0.02 \times \frac{9}{12} \][/tex]

Let's perform the multiplication step by step:
1. Calculate the time fraction in years:
[tex]\[ \frac{9}{12} = 0.75 \][/tex]
2. Multiply the principal by the interest rate:
[tex]\[ 1000 \times 0.02 = 20 \][/tex]
3. Multiply this result by the time in years:
[tex]\[ 20 \times 0.75 = 15 \][/tex]

Therefore, the simple interest owed for the use of the money is:
[tex]\[ I = \$15.00 \][/tex]

Thus, the simple interest owed is [tex]\( \$15.00 \)[/tex].

The simple interest owed for the use of the money is \$15.00 (rounded to the nearest cent as needed).
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