Certainly! To figure out how much of the first month's payment is interest on a [tex]$2000 loan with an annual interest rate of 9% APR, we'll use the simple interest formula.
The formula for simple interest is:
\[ \text{Interest} = P \times r \times t \]
Where:
- \( P \) is the principal amount (the initial amount of the loan)
- \( r \) is the annual interest rate (in decimal form)
- \( t \) is the time period in years
In this problem:
- \( P = \$[/tex]2000 \)
- [tex]\( r = 9\% = 0.09 \)[/tex]
- [tex]\( t = \frac{1}{12} \)[/tex] (since we're looking at the interest for just the first month)
Now let's substitute these values into the formula:
[tex]\[ \text{Interest} = 2000 \times 0.09 \times \frac{1}{12} \][/tex]
Carrying out the multiplication step-by-step:
1. Calculate the annual interest:
[tex]\[ 2000 \times 0.09 = 180 \][/tex]
2. Convert the annual interest to monthly interest:
[tex]\[ 180 \times \frac{1}{12} = 15 \][/tex]
So, the amount of interest for the first month's payment is:
[tex]\[ \$15.00 \][/tex]
Thus, the first month's interest is:
[tex]\[ \boxed{15.00} \][/tex]
