Let's calculate the amount of the 14th payment that will go to interest for the given installment loan with an outstanding principal of [tex]$1,000$[/tex].
1. Identify the relevant information:
- Outstanding principal: [tex]$\$[/tex] 1,000[tex]$
- Annual interest rate: $[/tex]9\%[tex]$ or \(0.09\)
- Monthly payment: $[/tex]\[tex]$ 95$[/tex]
- The interest part of the 14th payment needs to be determined.
2. Convert annual interest rate to monthly interest rate:
- The annual interest rate is [tex]\(9\% = 0.09\)[/tex].
- The monthly interest rate is calculated by dividing the annual interest rate by 12 (since there are 12 months in a year).
[tex]\[
\text{Monthly interest rate} = \frac{0.09}{12} = 0.0075
\][/tex]
3. Calculate the interest part of the 14th payment:
- The interest part of the payment is found by multiplying the outstanding principal by the monthly interest rate.
[tex]\[
\text{Interest payment (14th month)} = \$ 1{,}000 \times 0.0075 = \$ 7.50
\][/tex]
Therefore, the amount of the 14th payment that will go to interest is [tex]$\$[/tex]7.50$.
