To determine how much of the 14th payment will go to interest, we begin by acknowledging the outstanding principal amount and the annual interest rate provided. We aim to calculate the interest part of the payment specifically on the outstanding principal by the 14th month.
1. Identifying the Key Values:
- Outstanding Principal: \[tex]$1,000
- Annual Interest Rate: 9%
2. Converting the Annual Interest Rate to a Monthly Interest Rate:
Since interest rates are usually annual, but our payments are monthly, we need to convert the annual rate to a monthly rate.
\[
\text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12}
\]
Plugging in the values, we have:
\[
\text{Monthly Interest Rate} = \frac{9\%}{12}
\]
Expressing 9% as a decimal (0.09), we get:
\[
\text{Monthly Interest Rate} = \frac{0.09}{12} = 0.0075
\]
3. Calculating the Interest Component of the 14th Payment:
The interest for any given payment period is calculated as:
\[
\text{Interest Payment} = \text{Outstanding Principal} \times \text{Monthly Interest Rate}
\]
Substituting in the known values, we get:
\[
\text{Interest Payment} = 1000 \times 0.0075
\]
4. Solving for the Interest Payment:
Multiplying the outstanding principal by the monthly interest rate:
\[
\text{Interest Payment} = 1000 \times 0.0075 = 7.5
\]
Thus, the amount of the 14th payment that will go to interest is \$[/tex]7.5.
