To find out how much of the 31st payment will go to interest, we need to follow a few steps. These steps involve understanding the outstanding principal, converting the annual interest rate into a monthly rate, and using this monthly rate to determine the interest portion of the payment.
1. Convert Annual Interest Rate to Monthly Interest Rate:
The annual interest rate is given as 12%. This needs to be converted to a monthly interest rate:
[tex]\[
\text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12}
\][/tex]
Given that 12% annually is 0.12 in decimal form, the monthly interest rate would be:
[tex]\[
\text{Monthly Interest Rate} = \frac{0.12}{12} = 0.01
\][/tex]
2. Calculate the Interest Portion of the 31st Payment:
The interest portion of any installment payment can be determined by multiplying the outstanding principal by the monthly interest rate. The principal outstanding at the time of the 31st payment is [tex]$596:
\[
\text{Interest on 31st Payment} = \text{Outstanding Principal} \times \text{Monthly Interest Rate}
\]
Substituting the values we have:
\[
\text{Interest on 31st Payment} = 596 \times 0.01 = 5.96
\]
Therefore, the interest portion of the 31st payment, given the outstanding principal of $[/tex]596, is:
[tex]\[
\boxed{5.96}
\][/tex]
