To determine how much of the 15th payment will go towards interest when there is an outstanding principal of [tex]$848, we need to follow a step-by-step process that involves calculations using the annual interest rate and the number of periods in a year.
Let's assume the annual interest rate is 5%. Here’s how we proceed with the calculations:
1. Convert the annual interest rate to a monthly interest rate:
- The annual interest rate is 5%, or 0.05 in decimal form.
- Since there are 12 months in a year, the monthly interest rate is \( \frac{0.05}{12} \).
2. Calculate the monthly interest rate:
- \( \text{Monthly interest rate} = \frac{0.05}{12} = 0.004166666666666667 \)
3. Determine the interest for the 15th payment:
- The interest portion of a monthly installment is calculated based on the outstanding principal balance.
- For the outstanding principal of $[/tex]848, the interest of the 15th payment is:
[tex]\[
\text{Interest for the 15th payment} = \text{Outstanding principal} \times \text{Monthly interest rate}
\][/tex]
- Substituting the values, we get:
[tex]\[
\text{Interest for the 15th payment} = 848 \times 0.004166666666666667
\][/tex]
4. Perform the multiplication:
- [tex]\[
848 \times 0.004166666666666667 = 3.533333333333333
\][/tex]
Therefore, the amount of the 15th payment that will go towards interest is $3.533333333333333.
