\begin{tabular}{|l|r|}
\hline
\multicolumn{2}{|c|}{Installment Loan} \\
\hline
Principal & [tex]$\$[/tex] 5,580[tex]$ \\
\hline
Term Length & 4 years \\
\hline
Interest Rate & $[/tex]12 \%[tex]$ \\
\hline
Monthly Payment & $[/tex]\[tex]$ 147$[/tex] \\
\hline
\end{tabular}

How much of the 16th payment will go to interest if there is an outstanding principal of [tex]$\$[/tex] 4,112[tex]$?

Interest on the $[/tex]16^{\text{th}}[tex]$ payment $[/tex]= \[tex]$[?]$[/tex]

Round to the nearest hundredth.



Answer :

To determine how much of the 16th payment will go to interest given the outstanding principal of \[tex]$4,112, we can follow these steps: 1. Identify the principal amount outstanding: \$[/tex]4,112.
2. Identify the annual interest rate: 12%.
3. Calculate the monthly interest rate: Since interest rates given in financial contexts are typically annual, we need to divide the annual rate by 12 to convert it to a monthly rate.

[tex]\[ \text{Monthly Interest Rate} = \frac{12\%}{12} = 1\% \][/tex]

4. Convert the percentage to a decimal: To work with the interest rate in calculations, convert the percentage to a decimal.

[tex]\[ 1\% = 0.01 \][/tex]

5. Calculate the interest for the 16th payment: Multiply the outstanding principal by the monthly interest rate.

[tex]\[ \text{Interest on 16th Payment} = \$4,112 \times 0.01 \][/tex]

6. Perform the multiplication:

[tex]\[ \$4,112 \times 0.01 = \$41.12 \][/tex]

Therefore, the amount of the 16th payment that will go to interest is [tex]\( \boxed{\$41.12} \)[/tex].