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).
