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\begin{tabular}{|l|r|}
\hline \multicolumn{2}{|c|}{ Installment Loan } \\
\hline Principal & [tex]$\$[/tex] 2,610[tex]$ \\
\hline Term Length & 4 years \\
\hline Interest Rate & $[/tex]9 \%[tex]$ \\
\hline Monthly Payment & $[/tex]\[tex]$ 65$[/tex] \\
\hline
\end{tabular}

How much of the 22nd payment will go to interest if there is an outstanding principal of [tex]$\$[/tex] 1,581[tex]$?

Interest on $[/tex]22^{\text{nd}}[tex]$ Payment $[/tex]=\[tex]$ [?]$[/tex]

Round to the nearest hundredth.



Answer :

GinnyAnswer
To solve the problem of determining how much of the 22nd payment will go to interest, we can follow the steps below:

### Step-by-Step Solution:

1. Identify the given values:
- The outstanding principal at the time of the 22nd payment is \[tex]$1,581. - The annual interest rate is 9%. 2. Convert the annual interest rate to a monthly interest rate: - The monthly interest rate is the annual interest rate divided by 12. - Monthly Interest Rate = Annual Interest Rate / 12 - Monthly Interest Rate = 0.09 / 12 = 0.0075 3. Calculate the interest portion of the 22nd payment: - Interest for the 22nd payment is determined by multiplying the outstanding principal by the monthly interest rate. - Interest for 22nd Payment = Outstanding Principal * Monthly Interest Rate - Interest for 22nd Payment = \$[/tex]1,581 0.0075

4. Perform the multiplication:
- = \[tex]$1,581 0.0075 = \$[/tex]11.8575

5. Round the result to the nearest hundredth:
- Rounding \[tex]$11.8575 to the nearest hundredth gives us \$[/tex]11.86

Therefore, the amount of the 22nd payment going towards interest is [tex]$\$[/tex]11.86$.